Just chiming in on the winter coop. Unless you have a permanent roof over your run already, I agree, do not make more work for yourself. They will either decided to walk in the snow or not. I have a run that I wrap in painters drop cloth this last winter, but we built for that. Babying your hens will result in problems over the winter. Do not heat the coop only the water, do not leave a light in there. Seal for drafts, not for warmth. Unless you have naked birds, they should be fine. What part of the state are you in?
Chickens will fly over that fence when they decide they want to, clipping only way to stop that. Dogs with bird drive like ours can be trained to tolerate the birds, but I would never trust ours with them. Believing that I could would result in dead ones. Jim has a breed that will train to protect, I have a breed trained to flush and grab.