Many dog obedience trainers say your dog may see something new and just take off after it even though they have had training. Doghouses should be off the ground so the bottom floor is not wet or cold. Straw is a good insulator. Blankets and rugs can get wet from your pet's feet and the wet blanket will freeze. Then your pet will have to sleep on the ice.
Pets can get frostbite.
In severe weather bring your pet indoors to the garage, basement, or confined areas. Fleas can make your pet sick and anemic. Without treatment your pet could die. Flea dirt looks like salt and pepper. Use flea treatments carefully.