My parents have created a sort of blow gun device thatthey use to launch marshmallows at each other (but mostly me lately).
Perhaps if you found a nice bit of PVC pipe with a diameter close to the size of your preferred thowing snowball. Cut an opening in the toop of it toward the back with a cover that slides back and forth (like the chamber on a top loading type rifle). Connect an air compressor of some sort to the back end. Then drop the snowball in the chamber, slam it shut and let your handy dandy snowball cannon blow! top loading with a constant stream of air pressure might give you instant firing as you close the chamber. Then you just quickly pull it back open and drop in another ball.
Pardon poor stream of consciousness writing style. I'm kind of making this up on the spot. I don't know if it will work well or not, but one idea usually leads to another. I hope this crazy idea helps.
Happy pelting!