I'm in Minnesota so i know a little about cold and snow,lol,,,, Yep, you'll need a walk in PROPERLY VENTILATED coop. A lot of windows for LIGHT. A HEATER for the WATER. INSULATION would be nice also, but not mandatory. I don't know how many hens you have but, it's always better to go big. Most chickens in cold climates will want to stay in all winter and don't like snow. You won't really need the heat lamp for warmth. That's mostly for light so you get more eggs. As far as the run goes, there'll be so much snow at times you won't even see it in the winter. The closer you have your coop to the house the better,cause you'll have to shovel snow and hike out there everyday in some extreme conditions. I would also suggest you build it big enough to keep your feed in there too, maybe in a large garbage can. that will save you hauling it through the snowbanks everyday. I would suggest a gable roof of at least a 4-12 pitch or more. There is lots of info on this site that you can peruse and study till you come up with the perfect plan for you and your hens. I would say that VENTILATION is the most CRITICAL part of the coop in a cold climate. Chickens give off a lot of damp heat and you have to get rid of that or you'll be in serious trouble before xmas rolls around. Chickens can take a lot of dry cold, but damp cold will kill them in short order.
I'm not trying to scare you off but i been in this state for 60 yrs and hung with chickens of all kinds my whole life. Hope i helped you out. You can PM me anytime.