
This poor man is waiting in hospital after being found outside on a park bench. Note Sheriff's office next to hospital waiting room.
Most dogs and cats do not fare well for long periods of time in sub-zero temperatures. While I think most of the doggy clothing industry is pretty much nauseating and useless, some winter-wear is appropriate. Dogs wearing boots and coats will be more comfortable for longer periods of time in freezing weather, especially the thinner breeds like greyhounds and their ilk.
Take your dog in from the outdoors right away if you notice any head shaking, lifting of one or more paws, lameness/limping, or inactivity. If you tie your dog up outside in the cold, you should try switching places with your pet one day and see how comfortable it is. Again, some breeds tolerate the cold much better than others, especially the northern ones.

I think I'm going to &%$#*&! puke.