Beautiful!!
You will want to swap the roost for something wider though, I think... better insurance against frostbit toes. The wide side of a 2x4 (corners knocked back a bit if they're sharp), or a *wide* dead branch, like 5-6" diameter ish.
There is nothing wrong with a wooden floor. If you...
Ooooo, nice shed!
Really, if he wouldn't let you use the *whole* shed <vbeg>, your 4 hens would do quite well if you just ran a table type thing along the back half of the shed or one side, so the chickens could be underneath (that would be their indoor coop, with the A-frame tractor moored to...
Honestly my best suggestion is to look around real quick now (before the snow piles up so much you can't move things around) for a secondhand shed on Craigslist/kijiji/whatever. You could attach it to your A-frame there so that the A-frame serves as the run but the chickens can stay in the shed...