It isn't so much that Snowball struggles with his beliefs as that he works out his beliefs, the commands that govern the farm, and the best ways to implement them over time, and in contrast with others. In other words, it isn't that he struggles with his own beliefs that much, but rather that there is a tension between him and the world.

As for his beliefs, at various times he clashes with Mollie (over sugar and ribbon, as symbols of slavery). He articulates the seven commandments—and then they change. He argues for the windmill, and then it fails in Chapter 6 and he's declared a traitor.