Help!! I can't train my shih tzu, specially because of the snow, any suggestions?

I have a one-year-old shih tzu, she didn't grow up enough, i guess she is a puppy size and we really have a hard time when it comes to taking her out on the snow. We live in Colorado, so we get snow storms very often; I have been trying to train her, and i thought we were understanding each other until the snow came again and now we are back to the same painfull routine for both of us. My only solution so far has been to keep her caged so she doesn't ruin the carpet. I hate doing this specially because she doesn't understand the difference between a floor pad and her bed.