The coop should not be air-tight, that would definitely lead to frostbite.
Consider practicing the Deep Litter Method, a great example of working smarter, not harder.
Once a week, add a layer of fresh pine shavings to the top. Together with the pine shavings, your chicken’s poop will form a compost layer that fosters microbe growth.
Microbes cut down on harmful bacteria, and can also help prevent mite and lice infestations in the coop. For the kicker, composting organic matter generates much-needed heat in the wintertime.
It’s not hard to raise chickens in the winter, nor hard to keep them warm enough. Remember they have warm-down feathers that help to keep their body heat.