I live in western SD, and it is generally fairly dry, but we do get snow, and we do get cold weather.
In the run, I have two small shelters, I put shower doors in front of one, and plexiglass in front of the other. This gives them wind protection and on a sunny day, it is much warmer in there. It is not sealed, it is wide open on both sides. I don't try and trap the heat.
I put quite a bit of bedding in the run. It keeps their feet cleaner. If I hear that there is snow coming, I will pitch that bedding up into mini haystacks. After the snow, I flip that hay on top of the snow, and it encourages them to come out.
I don't have electricity - I use black rubber bowls. If it is sunny, I will fill the empty one, flip the frozen one upside down. The black will absorb enough heat that the ice falls out. But if it is cloudy, I just stomp it out.
Do look inside your coop when your birds are roosted. I like the roost to be away from the walls, and 12-15 inches above their head is the ceiling. This keeps their breath from condensing on the wall and ceiling before it leaves the coop.
Think DRY not warm, dry chickens are warm chickens if out of the wind.
Mrs K