I live in UP Michigan (Lk Superior) with ave winter temps 0-10s F and coldest temps to -30 F in late winter when nights are often clear. I use course dry pine and aspen chips in coop and run. Twice a year coop chips go into the run for a clean out, but I add leaves, chips, straw every couple of weeks to the run.
I buy clear vinyl shower curtains to tack over the north and part of southern run to block wind snow, leaving about 6 inches open at top for ventilation.
If ambient temps get to -10 or more I add an oil filled radiant heater to the coop to bring temp up a bit.