Please be very careful, Donna!

Unless I have to actually walk through several inches of snow, I don't wear winter boots, I wear waterproof hiking shoes. The treads on them are a lot better than most winter boots. I just bought a new pair by Merrill on clearance at ****'s for $15!

Depending on the floor under the rug, you could always try some double-sided tape to keep it in place if it keeps moving on you.