These animal names each represent a character or group of people during the Russian Revolution. Their names have great siginificance.
Snowball represents Trotsky who was a great military leader. Well, he had great ideas anyway. This name probably signifies the fact that the plans he made grew and grew and grew, but so did his troubles. Snowball being run off the farm is comparable to Trotsky's being run out of Russia.
Moses represented the Russian Orthodox church, or organized religion. Here is an interesting irony though, in the bible Moses was not a good speaker, he needed his brother to speak for him. Orwell could have used that particular biblical name because of the silencing done to the church.
Squealer, appropriately named, represented the media. Pravda was the news during the Russian Revolution that would spin the truth in such a way that the people believed all kinds of lies. Every squeal, although well taken by the animals, was entirely painful just like the sound. Lies hurt and Squealer was good at making them appear true.
Boxer represented the regular working class people. Many of these people lost their lives because they were the working class who were literally worked to death. The choice of the word Boxer to represent the working class is an interesting one because the Boxers went against the government. This Boxer stayed true to the government to the very end. Perhaps that's because this Boxer thought he was part of a revolution that did not turn out to be so revolutionary.