I have two dogs: a labrador retriever and a dachshund. The labrador retriever loves cold weather and snow. The dachshund hates it. When I let them outside on these cold days, the lab stays outside and runs around the yard. The dachshund travels the minimum distance to get his job done and returns immediately to the house.
Here is a picture of the lab after he came in from playing in the snow this morning. His face was covered with snow, but by the time I got my camera for the picture it had started to melt, so it does not show up so well in this picture. He looks happy anyway.