In Animal Farm, persuasion is used primarily by the pigs, most notably Squealer, for the purpose of maintaining total control over the other animals.

As a skilled public speaker, Squealer routinely uses his speeches to persuade the animals that the pigs are only acting in the best interests of everybody. This is shown clearly in chapter three when it is discovered that the pigs have taken the milk and apples for themselves instead of sharing them out equally. To justify this action, Squealer first claims that pigs need milk and applies because they are "brainworkers" and these foods have been scientifically proven to aid the brain. Secondly, he uses fear to stop the animals from voicing any complaints:

"Do you know what would happen if we pigs failed in our duty? Jones would come back! Yes, Jones would come back!"

Through a combination of false facts and fear, Squealer, speaking on behalf of Napoleon, successfully persuades the other animals to accept this unfair situation. 

Persuasion is used by several of propaganda's techniques through the pigs.

"Four legs good, two legs bad" is a slogan.

Blaming every bad thing that happens (the windmill falling down, missing food) on Snowball is called scape-goating.

I think the most effective tool that Napoleon uses often through Squealer, but even when Napoleon is the communicator is persuasive appeals. When Squealer gives facts and figures (that are lies) about how much better the animals are producing that is a logical appeal. When Napoleon uses his dogs to instill fear while he speaks, that is using an emotional appeal.

I would say that most of the persuasion is done by various pigs. It starts with Old Major, but then most of the persuasion is done by Squealer later on in the book.

Old Major persuades mostly with logic, I guess you can say.  He talks to the animals about their situation without really exaggerating.  He talks to them about how they are abused by humans.  And tells them there has to be a better way.

Later on, though, Squealer does most of the persuading and he does it through propaganda.  He tells lies about how well things are going.  He implies that there is no choice other than Napoleon -- it's either Napoleon's way of Jones's.