Sure, having a daytime high temperature of 10 degrees with a windchill (or, "feels like") of 13 degrees below zero is unpleasant--but we've had it much worse.
As I write this, Rockford's current temperature reading is -3 degrees, with a windchill or "feels like" temperature of -19 degrees. If you're feeling cold while wearing long underwear, winter clothes, a heavy jacket, hat, and boots--imagine how your dog must feel.