Hi Liz - first,
I'm in Minneapolis and I understand cold. There are lots and lots of us MN folks here at the BYC, as well as others in cold climates, so hopefully more folks will chime in.
I had a little trouble following the description of your coop, but it sounds like it's not going to be very warm. As mentioned earlier, a picture is worth a thousand words. Here's what has worked for me:
I have found that once the snow falls (and it STAYS here once it comes) my chickens don't like to go outside. The pop door is opened daily until the temperatures hit around 0F then I keep it closed. When we have a sunny/warm day - I'm talking in the 20s, I will force the issue and push them out. They tend to stick to the shoveled path and they like to sun themselves on my back step under the glass door - it reflects sunlight/heat. The ground is totally frozen a foot down, so it's not like they can dig below the snowline for things to eat... I'm sure they think it's boring.
My run is covered and nestled between my garage and the coop, so it's relatively protected. If you decide to roof the run (and I'm glad I did), then it is vital that you build the run roof with the ability to withstand heavy snow. I tried putting down some straw over the snow - it still blows in from the sides - but it froze quickly and they just weren't interested in venturing out, so I gave up and let them stay inside. Their choice - like I said, the pop door is open.
For the coop, they have 12 sq/ft per bird. That's an enormous amount, but it has served me well over the past two winters. They can stay inside for weeks/months at a time and be quite content, happy even. They have surfaces to jump around upon, windows to sun themselves and a light that runs early mornings and evenings to extend the daylight hours. I find that they seem to actually lay BETTER in the wintertime! My coop is a walk-in style with insulation in the walls and ceiling. I use 9-12 inches of deep litter in the wintertime. I have ridgecap/soffet ventilation that is open 365-24/7 and gable vents that are open until temperatures fall below 0. I run a ceramic heat emitter over the roost 24/7 from November through April and supplement with a second red lamp when the temperatures go below -15F.
Whether you decide to go with heat or not, you will need to consider how you're going to keep your water thawed. I use a heated dog water dish, and I love it, but it requires electricity. Water will begin to freeze in as little as 10 minutes here, so the heat source is pretty useful.
Ventilation is vitally important in cold climates and Pat's page is great. While it seems counter-productive to cut holes in your coop when the goal is to keep it warm inside, it is really important to give that moist warm air a chance to escape. Chickens are pretty tough, and can handle incredible cold (it's been -10F inside my coop many times, even WITH HEAT) but they can't handle the humidity and could end up with frostbite.
Hope this helps. Good to think about it NOW than in the fall when there are so many preparations in the yard to attend to before the snow flies...