It occasionally gets a little below zero up here, but as you said, not that often. It was 4 degrees above zero when I took this a few years back. I left the pop door open and gave them the option to come out or stay in. Since the wind wasn’t blowing hard they came out.
They were already outside when this 1” snow fell a couple of years ago. They just never bothered to go in.
I’ve been trying to think what I’d do in your situation for two chickens. I think I’d build a 4’ x 4’ box since plywood sheets are 4’x8’ and cheap 2x4’s are 8’ long so 4’ is a good dimension to work with. Elevate that about 2’ above the ground. Under the tarp it may not matter but I’d be tempted to put a sloping roof on it. Maybe make one side 4-1/2’ high and the other 3-1/2’ high. Yeah, sides, not front and back. You don’t want rainwater dripping on you when you open a door and the roost would be about 3’ off the floor on the high end and a foot away from the wall.
I’d have roof overhang to stop rainwater from blowing in, especially on the high and low sides, and leave about 3-1/2” (width of a 2x4) open on top of the walls for ventilation. Again, under the tarp you might not need an overhang. You could even leave all the walls open at the top. If you consider your pen predator proof you are OK but you can always cover it with hardware cloth for added protection.
With that open under the top you probably would not need a window but if you do, cut a hole in it somewhere and frame in a piece of Plexiglas or something hard and clear like that. Where they can see out of it on the roost would work well. Mine like roosting near the window.
You need good access to clean it so I’d hinge the back so you can just drop it down. Put the pop door front or back but on the opposite end as the roost.
Another option, probably easier, is to box in one corner of that dog pen. Use plywood, siding, whatever. All you are trying to do is build a box to keep the wind off of them but leave the top open enough that air can get out. Don’t worry if it is cold. They trap air in their down and feathers to insulate them. They keep themselves warm. Check out that first photo.
They probably will not want to move in there. They are used to sleeping outside. You may need to lock them in that coop at night after they roost until they get used to going in there on their own. I’ve had chickens get that message the first time I did it. I’ve had chickens take 3 weeks to catch on but if you are consistent the will catch on.
I can’t think of anything you can just buy and put in there for only two chickens without going pretty big. Maybe a big dog house?