I'm guessing you are in Nebraska but there is no guarantee with that. I remember someone on here that put the state they grew up in as their screen name, not where they were currently living. I'll assume your summers are hot and dry which is no big deal but that your winters can be relatively cold but not really that bad for chickens. You can have snow or cold winds which can have an effect. Mine really hate a cold wind.
If you follow the link in my signature you will see why I don't believe in magic numbers for how many square feet chickens need. I don't believe chickens can distinguish between coop space and run space. To them space is space no matter where it might be as long as it is available. All the run space in the world doesn't help them if they can't get to it because you lock them in the coop or snow or cold wind is stopping them from going outside. While I'm sure they really enjoy an hour or two of free ranging it really doesn't add to their space when it's not available. I don't consider your run space to be your limiting factor but I consider more space anywhere better as long as it is reasonable to add it.
Chickens tend to avoid snow when they wake up to a white world. It's not the snow they hate but the change. Often some of my chickens will go outside after the snow has been on the ground for a few days and they get used to it but even then it's usually just a few, not all. Mine refuse to go outside if a cold wind is blasting them. If you can build your run so it keeps snow out, at least part of it, and you have a wind block so a cold breeze is not blasting them your run may be useful, but if not your limiting space may be your coop.
Some people do shovel their run for the chickens. That's too much work for me. Some people put plastic over the run to keep snow and wind out. Your run isn't huge, that may be an option. Others do other things.
If your limiting factor is an 8' x 8' coop there still is no set number where things go from heaven to a total disaster. If you go by that 4 square feet rule it's not that 16 would be great while 17 would mean dead chickens. It's more gradual. I find the tighter I squeeze 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 issues. I value that flexibility above the others. If I have flexibility my stress levels tend to go way down.
I don't know your goals, why you want chickens. Pets, eggs, meat, to breed, sell eggs, hatching eggs, or baby chicks. Will you be integrating chickens later, hopefully in better weather. It would be hard for me to come up with a number even if I knew a lot more about your goals, experience, planned management techniques, flock make-up, and so much more. My general suggestion is to start smaller than the maximum and gain experience. Make future decisions based on what you see.
As an example. If your goal is eggs, find out how many eggs you actually get and how that fits your needs. Learn the annual cycle of egg laying, it changes with the seasons and as they age. Some people keep their hens until they die of old age, even if they totally stop laying. They are basically pets with benefits. Some rotate out their flocks when egg production slows, often after three years but it can vary,. Some of us bring in new pullets every year and eat or sell the older hens to keep the flock relatively young and well-laying. Different management techniques could affect how many you start with.
I raise mine mainly for meat. I keep one rooster and 6 to 8 hens most winters but during the season I may have over 50 chickens out there, most growing to butcher age. Summer is when I need the room, not the winter.
I understand you want guidelines and I haven't really helped you with that. I don't know if you want full-sized chickens or bantams. With as little as I know I'd think you could go with as few as 6, but 12 would probably be OK. You'll just have to work little harder.