I have an idea now. (Be afraid!)
The cornucopia area on each map is filled with snow (or not filled, just there is a lot of it...) On SG4 that would be the area within the iron fence gate, on SG3 the whole inside mountain area, on SG1 and SG2, the area before the trees start and on Breeze the area in between the mountains.
Then, the only way to get snowballs is by making a shovel with any extra resources you have and spending a bit of time to harvest a bit of snow. Each snowball can do half a heart of damage, because its not hard to fire these things fairly quickly.
I think snowballs in all chests would be a bit crazy, but maybe a 0-4 in tier 2 chests would be a good idea too (in addition to this). That would make snowballs a fairly interesting item. You would also be able to get snow blocks, but that would be useless other than for show.
This would also make for a fun death match tool for teams that want something more interesting than fishing rods or shovels!