At the bottom of this I'll copy something I wrote in another post about coop and run space. A lot will not apply to your situation but you can maybe understand my comments. I'd give serious consideration to increasing the size of your coop to either 3' x 5' or 4' x 4'. Most building materials...
I think your idea of a 3-season coop will work, but I'm not an expert for your climate or the open-coop design. It may work for 4 seasons, but I prefer to keep life simpler and build a coop that can be closed off so there are no drafts that can hit the chickens but is very open at the top so...