I've seen most geocaches left up over winter and people actually sometimes do take a stick or something to poke through the snow. Of course, with snow, you have to worry about things getting wet. Ammo cans seem to be pretty waterproof, bison tubes if you go for a micro. Some homemade geocache containers just don't hold up to the weather. Home tuppeware if exposed seems to let moisture seep in. Today, I came accross a film canister that had a wet log.
For you, perhaps putting the cache in a tree somehow or up off the ground may help. I suppose it could still be placed at ground level, hmm...