This old photo is getting used a lot this time of they year. It was 4 degrees above zero when I took it. I leave the pop door open during the day and let then decide what they want to do.
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Your question about breezes and at night is a little harder to answer. A gentle air movement is good, it gets the bad air out and lets good air in. What you want to avoid is a strong breeze blowing directly on them. If you leave that pop door open and have ventilation openings on the roost side of the roost a wind from certain directions could blast through them. If there is not an opening on the other side it may not hit them. One popular coop design even up into Canada is to have the front of the coop pretty open but the roosts are back in a cul de sac where a breeze will not blow on them. I don't know if you could open a hole right above the pop door so any breeze that goes in would not make it to the back of the coop. That will depend on coop shape and how deep it is.
An easy way to provide good ventilation in winter is to have different openings above their heads and nothing down low at night. If you are leaving it open at night while you are away that's maybe not a good idea.
Since I don't know what your coop looks like or anything like that I can't tell you what will or won't work. But the cold is not much of an enemy, a direct breeze might be.
Where you could have an issue is that if the air in there gets high in moisture from their breathing, their poop, or maybe a water dish, that can lead to frostbite. The ammonia from decaying poop is lighter than air and can build up at the top if there is not a vent up there, but the leading cause of frostbite is moist air when the air temperature is below freezing. So at least a small amount of ventilation up high is a good thing. If you do see frostbite the normal solution is more ventilation.