As has been pointed out, Snowball does not actually return to the Animal/Manor Farm.
Napoleon and his cohort simply use Snowball as an image, a name, to which they attach all sorts of negative ideas.
Snowball becomes an ironic figure, blamed for being a traitor, it is Snowball who is betrayed by Napoleon. Snowball was honest, but his name is used in lie after lie by a regime that twists words to the point where they become meaningless.
It is important to remember that Orwell's novella is a fairy-tale-like story that is arranged for his satire on Communism. Snowball, of course, is Leon Trotsky, who was defeated by the Leftist side led by Josef Stalin, who later had him executed.
Snowball never returns, but is used as mentioned in #2 as a scapegoat after he is removed as an effective leader.
I don't think that Snowball ever does come back once he's run off the farm. Napoleon claims that he does, so in that way you could say he comes back for Napoleon's reasons. He "comes back" because Napoleon needs someone to blame for all the problems that the farm encounters.