The short answer - nothing. Aside from shoveling yourself a path and keeping any build up from threatening to collapse any part of the run, etc, there isn't really anything else you need to do. I do scatter hay/straw over the top of the snow in the run because this flock of birds is quite persnickity about getting their feet in the snow, and will hold up in the coop refusing to venture out - but my previous flocks have not cared at all and have come right on out in the snow. If the birds do opt to spend more time in side, you will want/need to adjust your coop maintenance accordingly to prevent it from becoming unsanitary - and keep an eye out for signs of any stress related behavior issues such as picking, etc developing.
What is your concern? What specific things are you worried about? A chicken coop should be designed to be outside wherever you live for 365 days a year. If you can give us a clue of what your coop looks like and why you are concerned we might be able to help you.
Unless you have something unique about yours that causes concern, you should do exactly what you do when it doesn’t snow, whatever that is.
Depends on the breeds of chickens you have. My uncle and aunt in Massachusetts had mostly cold hardy birds, Plymouth Rocks. They were fine with the cold weather. As long as they have a place to go to when the weather turns nasty, they should be fine. Eliminate drafts when possible, make sure they have dry places to go to. If we are talking blizzard here, you might want a heat lamp in the coop if they have to stay in it. A little warm oatmeal in the morning, make sure their water doesn't freeze up. Check on them regularly. They will let you know if they are in distress.