Chickens have extremely delicate respiratory systems so ventilation is absolutely critical.
If you provide it at roof-peak level (many people use soffit and ridge or soffit and gable venting), there will be no drafts.
Have a look at my brooder -- which is 4x8 and only 4-feet tall, but has 16...
Unless you live in an area that routinely spends extended time at or below 0F you don't need to keep your coop warm, just dry. :)
https://www.backyardchickens.com/articles/cold-weather-poultry-housing-and-care.72010/