Hi! I'm in the Twin Cities too. That cold kinda came up on us out of no-where, didn't it? I was just getting used to the 70 degree temperatures.... sigh.
BTW, your coop is very very cute.
I would recommend finding some plexiglass (home depot carries it, as does any good glass distributor - there's one on Excelsior in Hopkins) and using that to cover your windows. Make it thick. I can't tell from your photos how your screens are mounted, so can't give any recommendations for installation. However, having some natural daylight is definitely a plus on the upcoming FRIGID days when they won't really want to go outside so much. By the time the days are around 30, I close up my windows for the season. This is where your ventilation will become important.
Don't know how much hassle it would be to close up their popdoor at night, but it might be advantageous to keeping the coop a little warmer and not have cold air blowing up at them from below.
Looking at your photos, do they have any other ventilation other than the windows? If not, you're going to need to put some in. Could you drill in that space right above the windows? It's better than nothing. You'll want it high, so the warm, moist air can escape, and above their heads if possible. If you can make it with flaps, all the better.
I think your idea of closing up the run will make it more appealing for them to maybe spend some time outside once the real cold sets it. Additionally, it would probably keep some of those blustery winds from whistling beneath the coop, making it colder. Mine didn't care to go into the run in the winter, even tho it's covered. I've considered closing up the western and northern sides to keep the snow out, but it hasn't happened yet... we'll see. Either way, make sure you leave a little gap at the top, or leave one side open, so that isn't sealed up in plastic and the air can circulate keeping it from getting too moist inside.
PM me anytime if I can be of help!
ETA: I just checked out your page and looked at the bigger photos. I see that you have two little round vents in the gables. That's not a ton of ventilation - you may find that once you close up the windows, you're going to need more. I had those little steel vents too -- they look great, but weren't quite enough for the wintertime when the rest of the coop is closed up. We ended up using white return air vents from Home Depot. And then made flaps for the inside so that they could be closed up temporarily when it gets really cold. It has worked for us. HOpe this helps.