The good news is that those super cold clear days usually have sun like you mentioned so the birds can sit in the sun in front of the windows or can go out into the plastic covered run where it is warmer during the day if they like. The first year I had a run made from cattle panels covered with plastic and the temperature would be 90+ F when it was sunny, but then plummet when the sun went down. I didn't think 120 degree temperature swings were good for them, so I took the door off and left the end entirely open

That worked much better and I still do it that way. Cattle panel hoop houses with greenhouse plastic make great windbreaks and provide a nice snow-free area for the birds in the winter. My chickens don't mind the cold, but they don't like walking in the snow.