Draft-free doesn't mean sealing all gaps, it just means no wind strong enough to ruffle the chickens feathers when they're sitting on their roosts.
I'm concerned about your ventilation. You need 1 square foot of permanent, 24/7/365 ventilation per adult, standard-sized hen -- best located above the birds' heads when they're sitting on the roost.
If you close the windows and cover the door to keep winter storms out, do you still have that much ventilation up top?
Tip, the ones I bought from Lowes and used on the coop doors are not good. The shank isn't solid so the carabiners catch when I'm trying to open the door. (Of course what I can barely get open a raccoon probably can't open -- but it's irritating).
View attachment 2851943
These ones from Amazon look like overkill, but they cost less, operate smoothly, and take any size carabiner.
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https://www.amazon.com/dp/B084TSCF4...jbGlja1JlZGlyZWN0JmRvTm90TG9nQ2xpY2s9dHJ1ZQ==