Silkiesisters, your chickens will be fine outdoors in the winter where you live. I know cause we probably live within an hour of eachother and my chickens absolutely go outside in the winter.
Get your feeders and waterers outdoors and make them come out, even if it's just for an hour each day. They should be A-OK. The worst thing I've ever seen is the tinsy-tiniest bit of frostbite on the tips of big single combs. Otherwise, even if they don't LIKE being outside, they will be OK being outside.
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Proof. NEOH winters feel brutal to us humans but they're downright balmy for chickens. Not like canadian winters. My chickens were thrilled to come outside yesterday morning and today even though they're the coldest days we've had all year.
Just tarp off a roof on part of your run to keep the snow out if they're picky about snow. But the cold will NOT bother them.
As for moisture, at this time of year I struggle with it too. I've had no losses, illness or injuries from cold aside from the aforementioned tippy tip frostbite on big combs but I know what you mean about the bedding being awful. I like to clean my coop out in november to be ready for the cold, after the mud season starts to go down a little.
I find that newspaper absorbs the moisture better in the coop, but clumps more. It's best to have a variety of shapes and sizes in your bedding if you're not cleaning it weekly. These days I use straw and leaves mostly with a little shredded paper. I find that helps a lot. Once the frost sets in it's not a big worry anymore.
The plastic is going to make it worse, not better. The wood walls can breathe a little, the plastic can't. The plastic over the chicken wire wall might be preventing some useful air exchange like using an open air coop.
Instead of plasticing over that wall can you build out, outside, away from the wall to give that wall a wind break but still allow free air exchange? Like give it an extra big roof and then a couple of light walls sticking out so wind can't hit it directly but it's still open.
I know you're trying to make improvements, but here's a question for you to consider as well... Have your birds ever actually had trouble with the environment they're in? Illness? Frostbite? Or are you just trying to prevent future issues you haven't seen?