Where does Snowball go after being expelled by Napoleon?
Good question! Orwell does not make it clear where Snowball escapes to after he squeezes through the hedge. Napoleon uses this mystery to his advantage by blaming all negative happenings on the farm on a ubiquitous Snowball. In Chapter 7, the narrator explains that
"All this while no more had been seen of Snowball. He was rumoured to be hiding on one of the neighbouring farms, either Foxwood or Pinchfield."
The mystery of Snowball's location works well for Napoleon. If his dealings with Foxwood fall through, he blames it on Snowball's presence at Foxwood. If his communication with Pinchfield is stifled, it is because Snowball actually went to Pinchfield.
Orwell does not leave Snowball's final destination a mystery simply for the convenience of his plot; rather, he is portraying Trotsky's fate. After working tirelessly for Lenin and Stalin's cause, Trotsky was run out of Russia by the secret police, and rumors abounded as to where he might be. Most believe that he was murdered in Mexico most likely by KGB agents.
Snowball's real location remains a mystery after he is run off the farm by Napoleon. We never know if he is dead or alive, and it is difficult to imagine where he could find a comfortable home, now that the other farmers know he is a revolutionary.
However, none of the matters. Once Snowball is gone, his status becomes mythical or archetypal. This means he becomes not merely a pig, but The Scapegoat. He becomes the symbol of all evil, of all betrayal, of all the animals have to fear. He becomes bigger than life, capable, ludicrously, of any and all crimes. Whenever anything goes wrong, we can be sure that the pigs will explain that Snowball is behind it.
Of course, we know that the real Snowball, while not perfect (for example, he goes along with the pigs having extra privileges), is a sensible and intelligent pig who had the best interests of Animal Farm at heart. He worked hard to protect it and make it stable and prosperous.