There is no magic number that covers your question. It depends on the size and personality of the individual chickens, flock make-up (multiple roosters, broodies with chicks, are you integrating new chickens at this time), even how many total are in the flock. My answer is always going to be to provide as much space as you reasonably can.
That rule of thumb of 4 square feet in the coop with 10 square feet in the run is a real general thing. It will keep practically everyone out of trouble in a real wide range of circumstances. It is set up more for a fairly small flock in suburbia. It has to be overkill for a lot of people so it will protect practically everyone.
I don’t even know a lot of detail as to what your circumstances are but I’m confident mine are different. I don’t get a lot of snow here and it sounds like you do. It sounds like you are in suburbia. I’m not. I’m not going to try to give you a hard and fast number.
Is it possible to provide a space outside where you can keep the snow out? Don’t forget how heavy snow can be if you try to cover a space and snow can blow in from the side. It’s not just how much space they have but the quality of the space. If you can provide a place where they can get away from each other it can really cut down on behavioral problems. Chickens have developed ways to live together peacefully as a flock once they get the pecking order settled. One of these ways is for the weaker to run away from the stronger if there is a confrontation. Or they just avoid them altogether. A separate space could really help with the avoid part of this.
My chickens generally don’t like snow when they first see it, but usually after being exposed to it for a couple of days, they will get out in it to forage if some grass and weeds are sticking up out of it. I’ve even had a couple wade through 9” of snow to go check out the compost pile. But the chickens in this photo proved this wrong. That’s about 1” of snow that had fallen in the previous hour or so.
