I am in northern Quebec, so I understand your worries. -3 is just the beginning. I can hit -35 or even -40 quite a few times in a winter.
If you can get the coop inside another building to cut the cold that will go a long way. That also means they can go out of the coop in winter to walk around a little.
You'll want to insulate the coop somehow, even if it is inside a bigger building.
Anything that can be recycled into insulation can help. By the way, you can insulate from the outside too, if easier. Old carpets, tin from an old roof, plastic sheets (hardware store type they use over materials in the outside lots can help cut the wind). If you can put something up against the wall, then cover it so it stays dry it I'll help. (Picture a garbage bag of plastic bags from your recycling bin, and then cover it with some plywood. You've created a block for the cold. )
I created a covered run for them from some old windows and wood from an old building. I had some old insulation I put in garbage bags, pushed them up against the walls, and then closed the wall with wood, it helps.
Water dripping into their space is a bigger problem than I expected, if it drops inside and makes ice, that keeps cold inside. Recall that the fridge used to be called the icebox and was just a wooden box with a big ice cube inside and it kept everything cold.
Also, the floor is more important for them than for you, so if you can put a false floor on-top of your normal floor then your straw on top, that will be warmer for them. A cold floor is a bigger problem than anything else because their feet are the most cold sensitive part of them.
If you know someone who can take a few, it it be easier to integrate your old hen to the new flock, but if you leave her with a few new friends that would be nice. There will be some fighting, let them sort it out, only intervene if you see blood, anything shy of that is normal and necessary (sorry) it is their nature, they need to establish the pecking order. The sooner it is done, the easier it is for them. You can call time out and send them back to their corner like a boxing match, but the fight is normal.