Are you snowed in? Why not turn to YouTube for practical advice on flinging snowballs using a slingshot?! It requires the right slingshot, and it's cold work, but it can be done.
In this video, Joerg Sprave demonstrates his snowball slingshot technique. It boils down to a BB-style slingshot equipped with a larger pouch, and a little flick of the wrist.
Sample line: "Large forks -- all they do is, they weaken the slingshot, because they put enormous strain on the wrist. ... What you need is a fairly large pouch."
Use your newfound powers for good, people.