Providing a sheltered/covered area in the run helps too. I have a piece of plywood on the side the prevailing winds come from. Part of my run is covered as well. This gives them shade in the summer and a dry spot from snow/rain. If the chickens have a dry area outdoors then they will track less snow/moisture into the coop, so the air in the coop will stay drier and warmer. On the coldest days I'll be sure to scoop out the poop from under the roost and thrown down an extra inch or two of bedding, again, as others have mentioned, getting moisture out of the coop. Food and water goes outside almost always. I don't want the water in the coop, I don't want to invite rodents in the coop, also it encourages the chickens to venture outdoors. A chicken that goes in and out to eat and drink is active, it's not just sitting still, it gets the blood flowing, helps them stay warm. If I notice the birds have not ventured out all day in a blizzard or something, I will put the food and water in the coop for a few hours and lock up the door for them, but generally the door is always open (at least to start the day) and they get to decide when to go out and for how long. The virtually always go out at least in the warmest part of the day, even if it's well below freezing.
So yes, tip one is keep things dry as best you can.
Tip two is watch your birds and their behavior. Check on them often. You will be able to tell if they are doing well or if adjustments need to be made. Are they eating and drinking? Are they walking around? Have they left the coop? Have they left the roost? Are the huddled together? Is the water frozen? How do their combs look? (also collect eggs often before the freeze if possible)
So yes, tip one is keep things dry as best you can.
Tip two is watch your birds and their behavior. Check on them often. You will be able to tell if they are doing well or if adjustments need to be made. Are they eating and drinking? Are they walking around? Have they left the coop? Have they left the roost? Are the huddled together? Is the water frozen? How do their combs look? (also collect eggs often before the freeze if possible)