They don't even call them blizzards anymore. In North Dakota, they are called major winter weather events. With the right clothing and a good attitude, bad weather hunting can be very enjoyable. My LL Bean Hunting pants were waterproof, windproof, and very light. I did not even wear long underwear. My Orvis wool Elmer Fudd hat, or something like it, was absolutely mandatory. Wool and Gore-Tex about seven layers deep, constituted the upper body wear. The only weak point in my system Is my gloves. I wear Orvis deerskin hunting gloves. I don't like thicker gloves because they don't have the touch. I was right on the edge of being too cold on the fingers. In fact, I may have to change my gloves. I am still looking for a suitable pair for cold weather.
As far as the dogs are concerned, the weather really did not bother them at all. Even Ruby, who is the skinniest of them all and went through the ice into the creek, came up and hunted like a champ after that. I watched her closely and she was doing just fine. Another problem you may encounter, is keeping the dog water thawed out. I took care of that by putting the container inside the truck. If you're gone long enough it will freeze. But even at 8°, we had no problem.
I would not want to hunt in this weather daily. But the occasional storm provides a lot of opportunity. We found roosters clustered together in shelterbelts and in the cattails.