HI.
Another thing to try is the Self-Stick Stretch Bandage that you can get in pet pharmacy stores...sometimes used to wrap horse's legs...but you can get smaller sizes. They come in all colors...
It only sticks to itself, and not your dog's hair!!! And, its stretchy....so, you can wrap it around the foot to keep the snow out at least, or up the leg to keep the snowballs from forming, if you don't have a snowsuit.