It would be uncomfortable to you but it isn't to chickens. They are equipped to handle it. The simple answer is that is where they want to be. Otherwise they would be somewhere else.Why on earth are they sleeping ... on the cold wet earth????? And against a chain link fence where a predator that does make it's way past the dogs could grab them through the fence??? The roosting bars were mostly free with two hens on each. I don't understand why they'd choose to sleep in such inhospitable conditions as wet cold ground when there's cozy dry house to sleep in.
I lived outside Fayetteville for several years so I have an idea of your climate. I grew up in the ridges of East Tennessee which has an equivalent climate. Mom and Dad had chickens sleeping in trees in the winter. Even temperatures below 0 F (-18 C) didn't bother them. Very few people on this forum have seen how chickens manage in that kind of weather. It gives you an appreciation of what chickens need versus what we think they need. Much like the wild birds that overwinter there, I think your chickens have the option to find a place that protects them from the weather according to their needs. Most of the flocks of people on here don't have those options, they are restricted to pretty small and often barren coops and runs. With that tree stump in your run I envision something really nice.
Yet they lay in there so the henhouse isn't totally evil. I suspect that reaction had something to do with them not liking change (being locked up). Chickens can be pretty adaptable so if you give them a little time they should calm down before too long.I tried this several weeks ago (all of mine I adopted after they were already grown and accustomed to being fully free range). The result was a bunch of freaked out birds frantically trying to escape the evil henhouse.
I can't find where you said how big that coop is. With two roosts 6 feet long it implies it's only 6 feet wide. It may be too small to leave them locked in there for long. That may have had something to do with them not liking being locked in there during the day.
I'm not sure how predator proof your chain link run is, that would be my concern. You have fox, wildcat, raccoons, and other critters that can climb chain link. Owls hunt at night. If you are not going to lock them in the coop overnight if they go in there it really doesn't matter, but yours can be trained to sleep in there. It will take some work and consistency on your part. There is nothing in their instincts that tells them they need to sleep inside a building. You have to get them in the habit of sleeping in there.
If you can't lock them in there for weeks on end, you can go out when it gets dark and they go to sleep. They are usually pretty easy to catch then. Lock them in the coop overnight. It may take a while, even weeks, but they should eventually all put themselves to sleep in there. That's the way I'd approach it.