Chickens can lose toes to frostbite, as well as parts of their combs and wattles. As long as they have a draft free coop that's adequately ventilated to take shelter in, they should be fine. We don't heat the coop.
Most of the winter we leave the pop door open and let the chickens decide whether they want to be inside or outside during the day. As it gets colder, they come back inside when they get too cold, to warm up. Later, they'll go back outside. When it gets really cold, ours choose to stay indoors.
I like a wide 2x4, wide side up, as a roost. It helps them cover their toes with their feathers while they roost. On really cold days, mine will sometimes go to roost during the day for a little while. Other times they'll just rest on the floor during the day, covering their feet with their feathers. The rest of the time they walk around normally.
We close the pop door during blizzards or really bad storms. Usually if the high for the day is going to be below zero, too, although we wouldn't have to. We only do it because our particular chickens don't like to be out when it's that cold and it keeps the coop a little cozier.
Some chickens hate walking in snow and some don't mind it that much. If you get deep snow, you'll need to shovel for the chickens, unless you have a covered run. There's only so much they can do with those short legs.
If you have young chickens that have never seen snow before, keep an eye on them the first snowfall or two. They can take cover when the snow starts and get stranded somewhere, afraid to come out and walk on the snow. They just haven't learned what it is, yet.