It can get frustrating trying to post photos. Sometimes that comes from the device you are using, some browsers work better than others. At least you figured it out.
What are the dimensions of your coop, the coop section itself and the run section? Just saying small doesn’t help a lot.
I was surprised when I checked on your temperatures and snow. Your cold doesn’t show a lot of problems for chickens, they should be able to handle your extremes OK, but I was surprised at how much snow you get. I thought south of Dallas you’d get a lot less. Why snow is important is that chickens don’t like change. When they wake up to a strange white world they usually take a couple of days to build up the courage to get out in it. I’ve had chickens that were outside when snow fell during the day and they never bothered to go in, the snow itself didn’t bother them. It is the change to waking up to a white world that confines them to the coop. You might want to put plastic or something around that coop/run you have now to keep snow and wind out to give them more room in the winter. They don’t like a cold wind hitting them either.
Heat in summer is going to be your real enemy, not cold. They need as much shade as you can manage. A covered run will help, but a lot of sun comes in form the side. You might want to cover the south or especially west side of what you wind up with to block that hot afternoon sun.
I’m not a believer in magic numbers for chickens, 4 square feet in the coop plus 10 square feet in the run for example. There are plenty of people on this forum that provide less and do OK. There are also people that provide that much room and don’t have enough. There are so many different factors involved like flock make-up, climate, your management techniques, age differences, whether or not you integrate or allow a broody hen to hatch and raise chicks with the flock, and many others that no one set of magic numbers cover us all. From what I can see, yours being all the same age and all female, you probably don’t need that much room. If you ever add new chickens that could change quickly though. I’m a huge advocate of giving them as much room as you reasonably can. That’s for your benefit as much as the chickens if not more. I find the tighter I pack them the more behavioral problems I have to deal with, the harder I have to work, and the less flexibility I have to deal with problems. I make my life less stressful if I provide more room.
For example, the less space you have the more the poop is concentrated for the same number of chickens. I believe you need to spend as little of your time handling chicken poop as you can manage. The tighter your space is the more poop you have to handle. That’s called working harder and if it starts to smell from being so concentrated it’s stressful.
You seem to be more flexible on the number of hens you’ll keep than on that 4x4 pen. Sounds like you already have it. Does it have a gate so you can get into it? You need to be able to access all of your coop and run.
Another reason that the magic numbers don’t work is that the quality of the space makes a difference. Sometimes chickens just need a little personal space, especially if one of them is kind of aggressive. That’s why I’d like to know the dimensions of the coop you have now. If you put your kennel next to the coop, they’d have the small coop section where the nests and roosts probably are, the area in the run part of your coop, plus the 4x4 dog pen area. That might or might not work for three hens though it is tighter than I’d want. They would have areas they could go to get away from a brute if they need it. Most hens are not brutes but occasionally you get one that is. That’s another reason the magic numbers don’t work, personality of the individual chickens makes a difference.
I understand your desire to have a cover on the run. The bigger the run the harder it is to cover, especially if it is kind of wide. A 10’ x 10’ is a lot harder to cover without the roof sagging a lot than a 4’ x 10’. You need to be able to walk in the run without bending over or crawling. You might try Craigslist to see if you can come up with free or cheap fencing materials like dog kennels to make a bigger run.
Will what you have work for three hens? I don’t know. It’s not as horrible as some people would have you believe but it’s still tighter than I’d want. If your hens turn out to be fairly mellow, and most are, they should be OK but you might spend more time and effort on poop management than I’d want to.
Good luck!
