Not sure where you are located or how hot it actually gets. You can edit your community profile under “My Profile” at the top of this page to put in a general location. That does help with a lot of questions. I don’t know how cold your winters get or what you consider hot.
I do agree that heat kills a lot more chickens than cold. I’ve seen chickens sleep in trees in zero Fahrenheit weather. Those trees were in a protected valley, had some real thick branches, and the chickens could move around a bit to get out of the worst of the wind, but they did not get frostbite and certainly did not freeze to death.
The drafts you worry about in cold weather are winds moving fast enough to ruffle their feathers, which can happen in storms. Their feathers and down trap a lot of air which insulates them. A breeze strong enough to ruffle those feathers can release that trapped air. The added danger is that moving air can cause wind chill. That’s the danger of drafts. On the other hand, ventilation removes excess moisture which can lead to frostbite. Good ventilation without drafts hitting them I important in really cold weather.
In hot weather, a breeze hitting them feels good. Drafts are not a problem in hot weather, not at all. It’s really hard to have too much ventilation in warm or hot weather.
Be careful with a screen door. Don’t use regular screen. Instead use wire heavy enough a coyote, big dog, or big raccoon can’t tear through and make the frame strong enough they can’t destroy it and get inside. I don’t know if you can open those windows or not, but if you do they need to be covered with heavy wire too to stop predators.
Instead of a screen door, I’d suggest you cut out an opening down low, frame that in, and cover it with heavy wire, just like you would frame it for a window. If you wish, you could even make a flap you could lower in the winter.
All this assumes your enclosed run is not predator proof. If you are confident your run is totally predator proof against climbing, digging, and just strong ripping predators, then you don’t have to worry about all this.
It sounds like your set-up will be real nice for 3 or 4 hens, plenty of room. Those maple trees will help a lot in summer. If I may make a suggestion, consider using light colors for the roof and maybe even the sides to reflect more heat instead of absorbing it.
Good luck! I think you are going to have a good experience with your chickens. Glad you joined us.