I agree with everything that Twocrowsranch said.
My cot quail don't like the 4 walls...very few went in when I had a shelter like that. I've gone to a short 3 sided shelter, 9 1/2 inches in the front, 6 1/2 inches in the back, roofed of course. The roof dimensions are roughly 30'' wide and 22" deep. this shelter allows the whole covey to comfortably go in for bad weather. (Roughly 20-28 birds per colony)
Last winter, our cots actually "played" in the snow, instead of staying were we put straw down for them they would go to the snowy parts of the pen and burrow. The only losses we had were 2 older hens.
We don't use any supplemental heat at all and temperatures got to steady single digits with a few nights dipping below 0. Pretty cold for our part of the country.
Good luck with your birds, they should be fine.