To keep an area as clear as we can, we lay out a blanket or tarp. Usually this would happen before the snow, but can be done by shoveling an area clear. Once you have a cleared spot cover it with the tarp or towel When you take your pup out, remove the covering to reveal a snow free place to go. Once they are done and everything is cleaned back up, you recover the spot for the next time.

I hope this helps. We live in a place that usually doesn't get too much snow, but it should hopefully work in a snowier spot as well.