in speech and more inventive" than Napoleon. Snowball organizes the animals into committees. He created the military strategy known as Battle of the Cowshed. This battle was "a defense of the farm against the humans which proves useful when Jones and his friends try to retake the farm. Snowball shows his expert use of military strategy during the attack—which becomes known as the Battle of the Cowshed—and is later awarded a medal."

Snowball comes up with the idea of the windmill to produce electricity. Of course, Napoleon later steals his idea and takes all the credit for such an idea. Snowball represents the historical  figure of Leon Trotsky:

Like Trotsky, who was exiled from Russia by his former partner Stalin, Snowball is eventually run off the farm by Napoleon.

After Snowball is gone, Napoleon blames everything on Snowball. 

Squealer is a smooth talker. He has an answer for everything. He explains things to put Napoleon in a good light. Squealer is the propaganda chief for the pigs. He explains why the commandments seem to be changing. He tries to explain why the ambulance that takes Boxer away has a sign on it that says horse slaughterer. He is so fat by the end until his eyes are like slits. He has become a selfish, greedy pig like Napoleon by the end of the story. 

Animal Farm's third chapter goes into detail on the particularities of the first harvest. Generally speaking, almost all of the animals contribute at least to some degree (the cat is a major exception, always avoiding any work whatsoever), although the most labor intensive tasks tend to be given to the horses. As Orwell writes:

Boxer and Clover would harness themselves to the cutter or the horse-rake (no bits or reigns were needed in these days, of course) and tramp steadily round and round the field with a pig walking behind and calling out, "Gee up, comrade!" or "Whoa back, comrade!" as the case might be. (Orwell, Animal Farm,chapter 3)

Of all the animals, Boxer is described as the most laborious in his physical contributions to the farm, to the point that his efforts were, Orwell says, worth the equivalent of three other horses put together. Meanwhile, the pigs (in keeping with their role as the planners and organizers of the farm) supervise the work of the other animals, while also applying their intelligence towards problem-solving, in the case of any unexpected difficulties which might arise.

Even as the horses take the most labor-intensive tasks, the ducks and hens are described picking up any disparate grains or stalks which would otherwise go to waste. As Orwell puts it, "everyone worked according to his capacity" (chapter 3). That being said, there are exceptions. As has already been mentioned, there is the cat, who would always excuses to avoid doing any work, but there is also Mollie, who shows a tendency to begin work late and leave early. Meanwhile, Benjamin is described working "in the same slow obstinate way as he had done it in Jones's time, never shirking and never volunteering for extra work either" (chapter 3).

This first harvest after the Revolution emerges as the high-water mark for the animals on the farm. As the story continues, a far more crueler and more brutal picture begins to set in, with the growing dictatorship of the pigs (and ultimately the dictatorship of Napoleon himself) exploiting the other animals on the farm.

There are various candidates for smartest animal on the farm, all of them pigs. The selection among the pigs really depends on one's definition of "smart."

Old Major is the visionary, the one who has worked out for himself the nature of the animals' existence and the forces that shape their lives. Although he is only present at the beginning of the book, his is probably the most powerful and insightful intellect.

Snowball is the most inventive and brilliant of the pigs. He is smart in the sense of being an ideas man, as well as, like Old Major, a utopian intellectual.

Napoleon has the most practical mind among the pigs. We might describe his variety of intelligence as "street smarts." While he lacks Old Major's breadth of vision and Snowball's theoretical brilliance, he is able to defeat his enemies by being more strategically-minded.

Squealer is an example of the type of intelligence which allies itself with power and provides legitimacy, while receiving numerous privileges. Unlike Napoleon and Snowball, Squealer is not a leader but is able to manipulate others into doing what he wants.

If one were to attempt to measure their intelligence by some method like an IQ test, I believe Snowball would score the highest of these four pigs and Napoleon the lowest. Conversely, if you measure "smartness" by practical success, Napoleon would top the table and Snowball would come last.

There are really two justifiable answers to your question, though I believe that there is one best answer.

Snowball was a brilliant pig. He made the plans for the windmill. He adapted the commandments, but Napoleon took everything Snowball did and manipulated it to his own purposes. Napoleon was the smartest pig on Animal Farm because he defeated and outmaneuvered Snowball.

Snowball wasn't "smart" enough to see how Napoleon was out-strategizing him. Napoleon saw well ahead of time that Snowball would be a hindrance to his own consolidation of power, so he prepared by taking Jessie's puppies. He trained them quietly and in private and eventually used them to drive Snowball from the farm.  

All of these maneuvers are a representation of (or allegory for) individuals from the Russian Revolution. Though Leonid Trotsky was a brilliant thinker, he was out-strategized by Stalin. Stalin used his position as General Secretary to appoint friendly (or pro-Stalin) individuals to government posts. Trotsky was eventually expelled from the party and the country. He was finally assassinated while living in Mexico.

In George Orwell's Animal Farm, we have three prominent horses involved in the story.

The two most frequently mentioned are the cart-horses Boxer and Clover. These two horses represent a mature, hard-working couple. Neither Boxer, the male, nor Clover, the female, are very smart, but they are very loyal, as evidenced by one of his mottos "Comrade Napoleon is always right" Not only are these two horses loyal, but Boxer was "as strong as any two ordinary horses put together." Boxer's motto, when anything goes wrong, is "I will work harder!" Even when Boxer is wounded in battle, he will not take a day off of work. Boxer's death in Chapter 9 is a moving and troubling moment in the story.

After Boxer's death, Clover continues to pass on information about "the principles of Animalism" and is a respected teacher.

The third signifcant horse mentioned in Animal Farm is a young mare named Mollie. She is like a young, teenage girl who is only concerned about what she will eat and what her personal appearance is. She is also a poor worker and would often make some excuse to get out of doing work. She also refuses to learn any letters except the ones that spelled her own name. In Chapter IV, she is found hiding in the barn during the humans' attempt to recapture the farm. In Chapter V, it appears that Mollie has become a traitor to the animals. She soon afterwards disappears and was never mentioned mentioned again by the animals.

The horses featured in Orwell's work are distinct in their own ways.  Each features a component that Orwell can see as being manipulated by those in the position of power.  Mollie's self interest and desire for more sugar is something that Orwell sees as being critical in undermining solidarity and valid demands for change.  Her scope of self interest is contrasted with the nature of Boxer, whose self sacrifice for the good of Napoleon or the state is astonishing.  Boxer's desire and compulsion to work tirelessly for his government is noteworthy, and Orwell feels that it is this authenticity that is easily manipulated.  When Napoleon makes the deal to send Boxer away, it is a sign that unlimited loyalty and blind faith are dangerous for the body politic to possess with leaders who are motivated by the consolidation of their own power.  It is this perception that Benjamin possesses.  Benjamin is skeptical of Napoleon's claims from the start and does not succumb to the vision being offered by the pigs.  However, Benjamin does little, if anything, about it.  His failure to act, no doubt cemented by his own cynicism, ends up emboldening the aggressors or the political system because it has no redemptive end.  That is to say the cynicism might help individuals understand the ulterior motives of government.  However, if individuals do not act upon this and do something about the state of affairs, having such brilliant insight is useless.  Benjamin understands what is going to happen to Boxer, but takes too long in being able to help his friend.  In the end, each horse possesses characteristics or qualities that might be good, but these composites have to be merged into larger elements in order for true and meaningful change to result.  If this does not happen, each separate personification can become an extension of political control, a puppet of those who are in the position of power.

In Animal Farm, the pigs are generally regarded as being the most intelligent of all the animals. This idea is expressed as early as Chapter Two, before the revolution takes place:

The work of teaching and organising the others fell naturally upon the pigs, who were generally recognised as being the cleverest of the animals. 

This idea is further reinforced after the revolution, in Chapter Three, when the pigs organize the other animals during the harvest, instead of doing any real work:

The pigs did not actually work but directed and supervised the others.

What these quotes show, then, is how the pigs exploit their 'natural intelligence' for their own benefit. Their intelligence  is used as justification for not doing physical labour, for example, and later, for eating milk and apples and for sleeping in the farmhouse. 

The only exception to this rule is Snowball who tries to share his intelligence by teaching the other animals to read and write and by designing a windmill which will function as a labour-saving device. But Snowball's democratic tendencies will not be tolerated by the other pigs, particularly Napoleon, and he is driven to exile in a brutal display of force. 

Boxer, the cart horse, is the most heroic of the animals. He is a true believer in the ideals of Animal Farm and works incredibly hard for the betterment of the whole community. A very strong horse, he gets up a half hour before everyone else to begin work. He also volunteers for the hardest tasks. His motto when he faces any obstacle is always to "work harder." 

He is a brave fighter. Yet, when he accidentally kills a stable boy in the Battle of the Cowshed, he feels remorse. A large part of what makes him heroic is his moral decency. He truly cares about others, and unlike the pigs, he is not simply trying to help himself. He wants to work for the common good. Sadly, the pigs exploit him mercilessly.

I would also call the hens especially heroic when they stand up for their eggs. Napoleon has entered a contract that requires selling their eggs. They protest by perching on a high rafter in the barn. They lay their eggs there so that they roll off and smash on the ground. Napoleon goes after them ruthlessly—he cuts off their food supply—but nine of them die rather than capitulate. Napoleon does win, but not until after the hens have made a brave stand. 

It would be hard to argue about the importance of three of the main characters in Animal Farm: Napoleon, Snowball and Squealer. Napoleon is named after the famed French emperor, but he represents Russia's Joseph Stalin in the novel. Like Stalin, Napoleon ruthlessly has his opposition exiled (the Trotskyesque Snowball) or executed, and he double-deals with his neighbors Pilkington and Frederick (Germany and England). He embodies the name of Napoleon--corrupt and power-hungry. Snowball is based on Russia's Leon Trotsky, who is forced from power by Stalin, just as Snowball is run off the farm by Napoleon. Snowball is blamed for all of the farm's problems in absentia, just as Stalin used Trotsky to cover his own mistakes. Squealer is the leader of the propaganda arm of the farm, the equivalent of the Russian newspaper Pravda. Like Pravda, Squealer represents the truth, but little that comes from his mouth is honest.

Napoleon,  Boxer, and Snowball are all capable of evoking feelings in the reader.  Napoleon is the leader who carries on Major’s ideas after his death.  Although he posts the Seven Commandments that initially suggest all animals will be equal, he immediately begins to make some animals more equal than others by taking the milk and giving it only to the pigs.  “Never mind the milk, comrades!”  cried Napoleon, placing himself in front of the buckets. “That will be attended to.” (Chapter 2) As the novel continues, he takes more and more rights from the animals, giving those rights to the pigs.   The reader, in turn, becomes more resentful of him as time goes on because he acts like the farmer they drove away.  “Even in the farmhouse, it was said, Napoleon occupied separate quarters from the others” (Chapter 8).  At the end of the novel, he is wearing clothes and walking upright.

Boxer evokes strong feelings of sympathy in the reader.  Boxer, the strong workhorse on the farm, never complains about his lot in life.  He adopts the phrase, “If Comrade Napoleon says it, it must be right.”  (Chapter 5).  When things go wrong, he just says he will work harder.  He eventually works so hard that he works himself to death and is sent to the glue factory by Napoleon. “They are taking Boxer to the knacker’s!”  (Chapter 9).  The horse who believed so strongly in Napoleon has been thrown away like garbage.

Snowball is the scapegoat for everything that goes wrong on the farm.  As readers, we resent Napoleon and Squealer for placing the blame where it does not belong.  During the election, Snowball speaks passionately about the building of the windmill, only to be chased off the property by the dogs.  The same evening, Squealer is sent to tell the animals that the windmill would indeed be built.  “That evening Squealer explained to the other animals that Napoleon had never in reality been opposed to the windmill.” (Chapter 6).  Snowball, from then on, takes the blame for everything that goes wrong on the farm.

Within the allegory of Animal Farm, the three horses have their own particular roles, with Boxer in particular representing the working class, while Clover and Mollie embody particular voices and reactions to the Rebellion (which, within the allegory, stands for the Russian Revolution).

Of the three, it is Boxer that has the greatest presence and role within the book, embodying the Russian working class. He is the strongest of the animals and commits greatly to the physical labor on the farm. At the same time, however, he is also a deeply tragic figure, who, after his tireless work on behalf of the farm, has his trust and loyalty repaid by being sold to a slaughterhouse. In this sense, while he embodies the working class, he also represents the Soviet Union's betrayal of that class, as well as of its own original communist ideals.

Mollie, meanwhile, can also be understood as playing a vital role in the novel's allegory, embodying those voices that rejected the Revolution and longed for a return to the aristocratic regime under the Tsars. However, she does not have as much presence within the narrative as Boxer and Clover do, as she departs Animal Farm in order to return to the humans.

Finally, there is Clover. On the one hand, Clover can be understood as a counterpart to Boxer, but on the other hand, there is a vitally different subtext to Clover's characterization and character arc. For one thing, she is portrayed as more intelligent than Boxer, and, moreover, as the story unfolds, she does gain an awareness that the promise of Animalism has gone unfulfilled, even if she struggles to voice where this failure has occurred and is unable to overcome the manipulation of the pigs. Furthermore, by the end of the book in particular, she is presented as one of the oldest remaining animals and one of the few survivors of the Rebellion. In this sense, she can be understood as being a historical witness, as one of the few voices from that original generation that is left.

Well, it looks as though, based on your examples, you are already on your way to answering the question!  There are not a lot of pigs who are known by name in the book so it is not a hard one to research:

NAPOLEON: Napoleon role is as a authoritarian figure on the farm.  He is the mastermind behind the pig's ability to control the farm.  If you are considering the Russian Revolution, Napoleon represents the "Stalin."  In the end, he is the craftiest of all the pigs.

SNOWBALL: Roughly the "Trotsky."  He is intelligent and passionate about his ideals and the direction he feels the farm should take.  He believes in the ideals of the revolution and acts courageously in battling the humans.  Unfortunately, though he is intelligent and has the best intentions for the animals on the farm, he is not nearly as crafty as Napoleon and therefore is destined to be "driven out."  He, too, is not without flaws...he quickly accepts the idea that the pigs are superior to the other animals.

SQUEALER: I wouldn't call Squealer "the liar."  He is a manipulator of information, not a pathological fabricator.  He shows how, using rhetoric, half-truths, and "spin," it is possible to control people.  His role on the farm is really as minister of propaganda.

OLD MAJOR: The original swine.  He is representative of kind of a mix between Lenin and Marx, in real life.  His role was as the visionary of the revolution.  It was his ideas that started the whole ball rolling. He is the ideological "heart" of the rebellion.   He is an inspiration.  Interestingly enough, Old Major is the animal who, aside from the bird, has suffered the least on the farm.  As a "prize pig" he has lived a pretty spoiled life, yet he is the one who thinks most of the injustices found in the farm.

MINIMUS: His role is kind of minor.  He seems to work with the "propaganda department" and is the one who comes up with the "new and improved" anthem for the farm.

I think that is all the oinkers.  Mmmm....bacon.

That's kind of a big question because the role of the pigs is one of the most important in the book.  Also, there really isn't a "bad" importance or a "good" importance, but there are ways that the pigs acted "bad or good."

The pigs do some things that are positive for the farm.

1. They are able to get things organized quickly because they are more clever.
2. They quickly begin to "right" some of the wrongs that were done by the humans.  The animals, at first, are better fed and happier because of the organization that the pigs are able to bring.
3. The pigs are also able, later, to arrange to trade with the humans for things not available on the farm.  Granted, that mostly turns out bad for the other animals (like the Chickens who lose their eggs) but the ability to deal with the outside world would be important for things like vet care.
4. Old Major, the grandest of the pigs, is the one who starts the whole ball of revolution rolling.
5. Snowball has some great ideas regarding farm government and inventions like the windmill.
6. The pigs organize the defense of the farm
7. The pigs can read and so they learn how to do things around the farm

The pigs also do some rotten things, or have a "bad" role:

1. They chase out Snowball
2. They arbitrarily change the rules
3. They pamper themselves
4. They sell the horse to the slaughterhouse
5. They train attack dogs to use against the animals
6. They adopt the bad qualities of the humans, and in the end, become like the humans they overthrew
7. They understand how to lie.

Overall, the pigs show us the good and bad parts of human nature.  They can be clever, brave, and hard working, but once they have too much power they become lazy, violent, racist (or is it speciesist?) and greedy.  There role in the book is to represent our leaders and how too much power can be a bad thing for people to have.

A much longer argument could easily be made that the pigs actually represent the communists in the Russian Revolution, and that Napoleon is a thinly disguised Stalin or something, but that wasn't specifically your question so I will save that for another day.

As a group, the pigs are undoubtedly the cleverest animals. They show this in the way that they take charge of the initial revolution against Mr Jones, masterminding the campaign against him. Thereafter they keep control over the other animals. Snowball in particular stands out as a pig of exceptional ability, not least in a military sense, although he finds himself pushed out of power by his rival Napoleon who is helped out by another pig, Squealer. Napoleon is not clever in the same sense as Snowball, who has a brilliant mind, but he is very clever in the way that he manipulates his way to supreme power. The pigs, largely because of this manipulative intelligence, manage to keep all the other animals down.

There are other individual animals that are intelligent but they are not able, or (in the case of Benjamin, the old donkey) not willing to work together as a group. If they had been, they might have been able to overthrow the pigs instead of letting themselves be oppressed by them.