If your nest boxes are on the exterior and you have no more than 4 birds, a 4X4 coop may be fine. As others have noted, you'll need more ventilation than what you've described. In your climate, I would add a window for extra ventilation and because your birds will probably spend a lot of time in the coop in the winter. I would use galvanized metal roofing instead of clear polycarbonate for the roof. The clear poly becomes brittle over time and the galvanized roofing is much stronger.