You could move the coop to the outside and connect it with a tunnel to the run,3 side plywood and 1 side wire. This would free up space in the run and keep you from getting poopy feet when collecting eggs. Add some branches and perches in the run hang the water and food will keep it cleaner. I...
For the winter I wrap my run with heavy canvas and I do the front with a clear shower curtain,keeps the snow and wind out and gives it a green house affect during the day. It actually keeps it warmer than having nothing but it still gets cold but it won't bother them as long as they can get out...
I used a 3 inch elbow,traced around with sharpie and used my dremile tool to cut it out,a little at a time until the fit was tighta little caulking on the inside
I hang a cabbage from a string,it swings around as they peck at it,just hang it high enough so they have to jump a little to reach it,it will keep them busy for hours.
New England here also,I wrap my run with commercial grade clear shower curtains keeps the snow and wind out and let's the sunshine in,actually stays a lot warmer,for water i use horizontal nipples in a bucket with a plastic safe stock tank heater it worked great and it got put to the test after...
I built a tunnel going from the coop to the kennel run,sandwiched the chain link in between the wood frame, this pic was still wrapped for winter but you get the idea.
If your ramp is anything like the one in the picture i would recommend a flat board with cleats going across and all the way to the ground. They are probably horrified of the angle and not having enough traction.
The roost should be at least a foot off the wall, if your going to use some type of poop board i would cover the ceiling with chicken wire because they will be all over the rafters and poop containment will be useless at that point.
I would put a couple of hot wires around the base of the coop,one good crack from it should keep the dogs from coming back, tractor supply has everything you need.