As the title says, it appears mining snow with a shovel drops however many layers of snow there is PLUS an extra snowball. So regular snow layers drop two, a full snow layer block will drop 9 (I think). All snowballs are server side, too, and not just client side. All can be used as per normal.
I've now tested this in both Singleplayer and Multiplayer and it does effects both.
Dupe of MC-61821