So, you're the dictator of a large, extremely diverse country, and you want everyone to pretty much believe the same thing, act the same way, and obey you without question. What are the methods in your bag of tricks to get all your peeps to toe your party line? Besides constant surveillance, violence is probably right up there at the top of your list. And we certainly see lots of that in Breaking Stalin's Nose. From the petty, casual cruelty of teachers to State-sanctioned killings, violence is an institutionalized part of the oppressive political system in Sasha's world.
War preparedness class and the snowball fights are ways that the children are systematically desensitized to violence.
Sasha doesn't seem to have suffered much violence in his life, which is something that separates him from the rest of society.