I've never heard squashing or squeezing when applied to snow in your hand. We pack snowballs, for example. In this case, I might say "compressing" – "compacting" doesn't seem quite right for some reason.
I agree that "squash" implies that you intend to make it as flat (or possibly as small) as possible. You can squeeze something a little bit. You can squeeze something gently. Squash is generally complete and forceful.