In Bedrock Edition, destroying top snow with a shovel yields 1-4 snowballs. Any other tool, even if enchanted with Silk Touch, destroys the snow and drops nothing. Snow drops one item of itself per layer when mined using a shovel enchanted with Silk Touch, except for 8 layers of snow, which drops a snow block. Explosions by TNT or creepers also cause snow to yield a snowball.
In Java Edition, destroying snow with a non-Silk-Touch shovel yields one snowball per layer.