I think with a wrapped run and the opening being into the run you should be ok.
Is the opening up high to the back of the coop still open or is it closed off?
Personally with three birds I would close it off to prevent an accidental draft/wind tunnel effect. You could make it a drop down triangle shape hinged at the bottom so you could still open it if you get some nice days.
I would do something similar with the side above the clean out door as well but in 2 sections for a more adjustable option. That way if you get some serious wind you can close off half of it.
I am of course assuming that the areas just under the metal roofing ridges are open. In the extreme weather you may find that it makes for a wind tunnel if you leave the large section open fully on even one side.
Your chickens should do fine without added heat. I know as humans we feel the cold much more than most critters so are inclined to think they are just as cold. So long as they are in good health and have good feathering they should handle the temps just fine.
(remember we make coats for US with feathers and theirs are built in )
I would not try to hard to get a greenhouse effect going since this can raise the temp higher than they are acclimated for. To hot inside then going outside is a temperature shock. In some cases it can cause them to drop feathers that they really need for the winter. I would not do it. My south windows are actually pieces of the siding in frames so I can open them in the summer or on nice days in the winter.
As to frozen water there is little one can do without electric heated water dishes. I have electric in the coop but keep the water in the run. I do not heat the water since the expensive heated dishes I had failed miserably.
I got dog water dishes from the farm store that are just plastic, nothing special and cost like 5 dollars each. I simply keep one set empty and change it out in the mornings. The empty get filled and the frozen get removed. If I need to get frozen water out of them due to extreme temps I slowly pour hot water from a milk jug over the upside down dish. The ice drops out easily enough that they are available for use withing a couple minutes. I wont bring chicken dishes into the house/kitchen so they are outside all winter. If it is sunny they thaw enough sitting in the sun to drop the ice out. (I turn them upside down in the garden on top of a paver to let the sun work on melting the ice out.) Last winter we had lows of -20 and this method worked for us.
I would also not worry to much about the access door being left open causing a cold source. Heat rises so that should be ok. Now then the only real concern leaving it open would be a predator finding a way into the run and no barrier to the chickens in its way. My run is chain link and the pop doors are locked from the inside every night. We have coons and fox in the area so I went with the "lock it or lose it" mindset.
I think you are doing well going into winter thinking about all the possible issues keeping chickens in your climate.