Weather is weather in my world, not good or bad, just weather.
I follow the Farmers Almanac, for twenty-seven years at this point, and it has been more consistent than most other sources. 
February is known for cold snaps, sometimes for days and sometimes for weeks. While it is hard on the paws, and hard on pasture animals, it is Mother Natures way of keeping other things in check. For example, to kill off pine beetles, we need a week or two of -13 to -31. To get rid of parasite eggs in the soil we need the opposite, super hot summers.
So you see, Mother Nature has her reasons.
 

These temperatures are inappropriate to be outside for any length of time, unless you have a for real northern breed, and then you better know what you are doing and why.
Going outside to potty and play a bit, if your dog is game for that, is a good thing, but short frequent sessions are far better than long ones. 
In these temperatures your dog can get frost nipped easily, and if running for a while, nipped on the tongue, roof of mouth, and throat.
It isn't a good idea to go distance from your home or car, into the back country when we have below zero temperatures. YES, I know I know, the ice climbers in Hyalite have their crag dogs running around while they are climbing in these temperatures, but all the same, it's wrong and puts the dog in danger of injury or worse. Climbers are geared up and dressed for the weather, their dogs are not. And I will leave it at that.
So extra bedding for your pasture animals, a bit more attention to open drinking water throughout the day, good food with lots of energy, and a nice warm place for your dog inside.
 

When we have cold snaps, training inside is super fun and you can make so much awesome progress on whatever it is you are working on, because you have no external distractions.
Check out our VIDEOS for ideas. Music and a warm house make for a great training day!