Yes! And I live in the Frozen Tundra. My first greyhound, Lila, had very thick, plushy fur like a bunny and she was always warm. She wouldn't move with a coat on unless it was below zero. She would usually get out of her bed to stretch out on the floor to cool off. She would get cold feet from walking on snow, but that was the only issue for her.
My current girl, Wiki, has sleek fur like a sea lion and doesn't run as warm as Lila. But she still pants on walks with a single layer fleece coat in temperatures in the teens.