Thank You. I couldn't have asked for a better detailed answer.Thanks for having your location available in your profile. That helps.
What do you want to use the run for if you free range all the time? The real question is how much time will they be locked in the coop and run. If they are only going to be in there for a short time, say while you treat them for mites or band them, it really doesn’t need to be all that big. If they are going to spend weeks at a time, it needs to be bigger.
You’re in Idaho. You are going to get snow and bad weather so they could be stuck inside the coop for a pretty good while. If you are using the run to help create some more usable outside space, it doesn’t have to be tremendously big to be really useful. Mine usually don’t like the snow initially but after a couple of days some will go out and roam in it. Cold weather itself doesn’t bother mine but they hate a cold wind. If you build the run with a top and enough sides to keep snow out, you’ve really helped yourself. But if they have some outbuilding nearby they can get to, the need for the run space in winter drops.
I’m a believer in providing as much space as you reasonably can, but keeping snow out of one can get expensive, especially if it gets wide where you have to span a distance and consider snow load. The bigger you make it the harder and more expensive it becomes to make it truly predator proof.
If it were me I’d consider something along the lines of an 8’ x 16’ run, with bigger better if that is a reasonable option. The 8’ wide because your coop is 8’ wide. That gives you a solid windproof side to your run. 16’ because I normally space posts about 8’ centers and most wooden building materials like 2x4’s are cheapest in 8’ lengths. That 8’ spacing is often a real convenient spacing to use, but if you are just using wire for the run, you can certainly change that.
With that flock this will give you more than you absolutely need. You don’t even have to completely keep snow out of all of it, just a few feet at one end. Since you have the rooster you just might hatch chicks so your numbers could grow, especially in the summer. And with it being a bit bigger than the absolute minimum, you have some flexibility if something happens. Say you find you have a predator problem and can’t free range for a few days while you take care of that problem? If it’s big enough you can keep them locked up for days or even weeks while you deal with that predator. Some predators take time to manage.