There used to be a couple of structures like that in a poplar grove across the road from us. The farmer responsible for them was Dennis Casey. They were used to acclimatize/feed ring-neck pheasants for a few days. The birds were brooded then raised in cages so needed to be watched until they decided to settle nearby. Feed was left after the release until the pheasants had discovered local sources. It was a hugely successful program and to this day we have ringnecks nesting on our property, even a cock who dances for my hens!
Wow! Great ideas...ok, to answer some questions:
They didn't have dogs. The compost bin is made of cinder blocks and is over by the garden. There is 1 'food' garden and several flower gardens in the clearing so I don't think they'd put 1 in the woods. It doesn't look like the ground inside the pen has ever been dug. there are no doors.
If nothing else, it looks like you have some pretty good usable lumber. When the weather gets warmer, it might be good to go out and disassemble it, and reuse that lumber on a new sturdy coop and a rugged well sized, covered run. I can't tell for sure what sizes you have there but it could be useful for siding on a new coop.
How much space to you have and how close is the nearest electricity? Power would be real nice to have in a predator rich environment to power motion lights and electric fencing.
Get the sketchpad out and do some drawings with a notion toward a permanent structure as opposed to anything mobile or approaching free range. Figure on roofing it, because in those trees you probably have owls and other raptors that like chicken as much as coyotes do. We had a Barred Owl carry off a 3 pound Koi and eat it at the top of a pine tree in our back yard. It was a big owl, and he tried to take one of the cats once too. Chickens would be no match.
Press on and do some planning for when the snow melts! There's a million and one ways of doing this and most of them are just excellent.
At the very bottom of the first picture is the log with the board nailed on it like a seat. Would you really sit that close if you're baiting bears? Or better yet...if I was baiting bears I think I'd want to sit inside!