If the body of the raccoon cannot come in, then the raccoon can only reach a certain distance-- maybe a foot or two. So if the chickens sleep at least that far away from the fence, the raccoons shouldn't be able to reach them.
I've also read of raccoons working together, so one scares the chickens into a corner and another grabs them through the wire on that side. The solution is to put piece of plywood against the fence on two sides of one or two corners, so the chickens have an unreachable place to huddle (because they aren't smart enough to just huddle in the middle out of reach.
I'm not sure what to do about mink, other than covering the whole thing in hardware cloth, because they can go through small spaces.
Chickens are usually fine down below freezing, as long as they are dry and out of the wind. But they will probably be fine sleeping in the coop you have, especially if you are able to leave the pop door open so they can go to the run just as soon as they wake up (maybe not, if there are mink around.)
And I would expect they can at least use the run in the winter, since it will have a roof.
I see trees, so there might be enough shelter from wind. But if you find wind whistling through the run in the winter, try adding tarps on one or two sides to block the wind. Be sure to secure them well, because a flapping tarp will shred itself pretty quickly, but they are an easy way to block wind that is also fairly cheap. Just expect to buy new ones each winter, because they will probably be in bad shape by spring.
I see you posted this while I was typing ideas about tarps

Maybe that can change if the weather gets bad, especially if you can make it look nice (green for Christmas? or orange for Halloween? Hang a wreath and some lights, or big pumpkins, or hearts for Valentine's Day so the tarp is a nice backdrop to a seasonal decoration?) Or maybe you could just put it up one winter day, and if someone complains you can assure them it'll come down when the weather gets nice. A tarp on the top like a roof will probably not work, because rain or snow can easily collect on top and get heavy enough to rip the tarp.
You won't want mud on the ground in that run, so I suggest you put in lots of materials like wood chips, pine needles, dead leaves, etc. They soak up some water, cover the actual mud, and give the chickens something to stand up on instead of having wet feet. They will also slowly compost, and chickens usually like to scratch through them. Just add materials as you can get them, and it's fine for them to end up piled a foot or more deep. Whatever kind of bedding you use in the coop can probably be put in the run too, when you clean the coop.