For some reason, people tend to give the dimensions needed for chickens in 2 dimensions, length times width. But really space is a three dimensional area. One needs to consider the height of the coop too.
In the cold north, frost bite is a real problem. And new people worry about cold, thinking that is the culprit. They imagine that if their birds are in a smaller space, they will heat it better. And then one considers the conflicting advice of having good ventilation and no drafts. But the cold is NOT the problem, it is the moisture. Dry, well fed birds can withstand easily negative 25 degrees.
When you set up your roosting area in either extreme, cold or hot, a bird needs to be able to be about 12 inches AWAY from the wall, and about 25 inches below the ceiling. When one crowds birds into a smaller area, what they produce is moisture, by breathing and their poop. In a small area with poor ventilation, this moisture collects on the walls and ceilings, and the birds sitting to close to each. Wet birds are cold birds, and very quickly sick birds. Think of 6 people in a car in the winter with no heater on. Within minutes the windows are fogging up. Even if the day is nice in the winter time, the day is short, and birds spend about 14 hours roosted up in the dark. That is a lot of time in a cramped, high moisture, low ventilation place.
Birds with space around them are much healthier birds, birds that are crowded are going to develop horrible habits, and be sick.
You cannot wish this away. I like the shed type house, big enough to nearly stand up in. It gives good space, with proper ventilation, it will keep your birds healthy.
Mrs K