I don't know how large your coop is, but I have a portable coop, quite small, and this year we only had a very mild frostbite problem once, despite being the coldest winter on record, and it was only for the rooster whose comb is enormous.
Each winter I wrap the wired part of the pen (their run) in heavy duty plastic (it looks like a small greenhouse) so that they can go "outside" without going outside. This keeps it quite pleasant even when it is snowing and blowing. I usually open up the door anyway as they like to step out if they can, but on a really cold day it lets too much icy air into the coop.
For the coop part itself, I went and bought a couple of sheets of thin, pink foam insulation at Home Depot and nailed them onto the coop with screws and large washers to hold it. Then I covered this with a tarp (though half the tarp has blown away). My coop is only made of thin plywood, but this thin foam insulation has kept the temperature at or above freezing inside the coop even on the worst nights ... usually on a typical cold night it is around 3 celsius in there, only after days of sustained cold does it dip to just around freezing at night, though it warms up in the day. When it is only a little below freezing (-5, -6 celsius) outside it gets a balmy 10celsius inside the coop at night. I have 11 chickens, so body heat is helping some, but it is much better than last year when I lined the coop with hay bales ... this worked some, but couldn't reach the top of the coop and they all got frostbite, the rooster especially bad.
The insulation cost less than $20 (it is a small coop) and has been just great ... I will just take it off in the spring.
Hope this helps.
I have a similar setup for one of my flocks. The house is 3'W X 4'L X 5'H, made of 2X4s and 5/8" (?) plywood, initially painted with Thompsons Water Seal. It roosts between 5 and 9 large birds comfortably (currently six LF Croad Langshans) The top is slightly sloped, and has hinges at the highest edge, so the top can be propped open as high as needed for proper ventilation. There is a 9"W X 12"H opening at the bottom for the birds to get in and out. The entire front comes off for easy cleaning. The perches are wide PVC pipe covered with foam pipe insulation (1-3 layers, depending on the birds), then tightly wrapped with vetrap. This way the perches are large, padded, and poop-proof. The vetrap is changed every 1-2 months, and the pipe insulation 2-3 times a year, as needed for cleanliness and padding. The perches are placed high enough that they're out of any draft from the bottom opening, but not so high that the birds are getting a cross breeze from the top. They're in that sweet spot of quiet but not stagnant air. The house sits on the ground. Inside the house, there is thick plastic directly on the ground to prevent moisture from wicking up, and that is covered by 8-12' of aspen shavings. The poop is typically picked up every 1-2 days in the winter, and every week in the summer, depending on how moist the poop is, how long the night is, and how cold the temperature is.
The house sits inside a 6'W X 12'L X 8'H predator-proof welded wire pen on a wood frame. The welded wire roof of the pen is peaked in the center, and has awnings that extend 18" out on all sides beyond the walls of the pen. The roof is covered with thick clear plastic. There is a large wire door on one end for people, and a small wire door beside it for chickens, both simply framed out with 2X2 wood. The pen has a dirt floor that is covered with a few inches of chopped straw, and the feeder and waterer are in the pen, elevated up on cinder blocks so the birds are eating and drinking at shoulder level, and the bedding doesn't get in the food or water. The straw is replaced whenever it gets too dirty or wet, typically every month. The birds are let out of the pen to free range every day, typically an hour after sunrise (the hawks and eagles hunt most aggressively here immediately after sunrise). During the summer the walls of the pen are left as just wire. When the wind starts blowing rain and snow sideways in fall/winter, I tie sheets to the wire walls. I tried plastic, but found that the wind tore it too easily because the wind couldn't go through it at all, and the humidity was too high in the coop. With thin cloth, the wind is significantly slowed but not 100% stopped, and the humidity can still escape, so the inside of the pen has gentle air movement without drafting, and it is amazingly warm. It's like being inside a tent. The plastic roof retains lots of heat, and the cloth lets out the moisture, so it feels 10-20 degrees warmer in the pen then outside in the open. Inside the house it's even warmer, despite the roof being propped open a bit. I would prefer to use clear plastic to let in more sunlight, but it just wouldn't work for my particular pen in this level of wind.
I built it in 1998, and the house and pen combined cost only a bit more than the tiny little premade "boxes of death" that so many feed stores (and Costco -- such a disappointment, as their products are usually good quality) sell now. It's not elegant, or even pretty, but it was quick to make, inexpensive, and after 16 years is still a comfortable and safe place for my birds. But I have started using earth tone sheets (light brown and greens) instead of white -- that was just too tacky, even for me.
