We used automotive stick-on seal as weather stripping. (Found next to the door seals). It seems to work better. I do like the idea of making it out of wood for sturdiness, but our application under a hinged roof wouldn't have worked.
We got the dog house made by the same brand and modded it into a brooder (It was a slightly broken return for half price). Sprayed all sides 2x with UV resistant polyurethane.
Added upper ventilation, under the roof.
That's one thing it seems you haven't worked on yet. You really need some ventilation right under the roof. On the run side would work well, where the roof is highest, especially if your run roof will cover against the elements. Otherwise you'd need a small awning over it.
Moisture and ammonia travel up, and where it gets very cold you especially don't want a humid coop for frostbite reasons. On the coldest days you could cover that existing vent which seems too close to the roost for draft purposes.