I do garden, and one of the main reasons I got laying hens was to make compost for me. Compost by the bag is expensive. The eggs are just a bonus. Well, and just the enjoyment I get from having the chickens.
Not too worried about the wind with whole leaves as I suspect they will stay within the chicken run fencing. Also, the chickens will tear it up and trample that stuff down in no time. Next spring it should have made some good compost for the garden.
It sounds like we share quite a few ideas. A couple notes, you probably know them, but I don't want to mess anybody up. Winter "composting" right on the garden like I do, makes it a water holding soggy mess on top. I take the chickens off in early March. I've got a big sheet of plastic I'll cover on area to dry so I can till, then move it down. Another thing, I start everything and transplant. So if anybody is direct seeding, what a plant might take, it could "burn" up an unestablished seedling.
Up North, ya know?

You guys got a lot shorter window than we do here in "O-hi-ah". I'd guess, at least your sun consideration would be easier, about all South or near straight up?
For your winter run, I'll get some pics of what I do, it's just 3/4 pvc electrical conduit hoops to a 8x8 frame of 5/4 treated, chicken wired for the summer, then some pool noodles to prevent the clear plastic from wearing through in the winter. Two guys can pack it anywhere, and it's cheap, under $150. I doubt it would hold up to your snow and wind. Give me a week, I sold one this spring, got sick again, and the new on is setting back here a half finished eye sore.
Sounds like I want to do this year. In the past, all leaves have gone directly to the garden, this year I will process them through the chickens. Should make some great compost with grass clippings, woodchips, kitchen scraps, and chicken poo all mixed in.
You probably know, at one point I didn't. From my own screw up, careful with the wood chips. If they are still recognizable as a chip, don't till them under.