I don’t get a lot of snow here. Usually if mine wake up to a new white world they stay inside for a day or two, but if the snow lasts longer than that a few will go outside in it, usually to forage on the dead grass or maybe weeds sticking out of the top. One winter I had chickens wade through 9” of snow to get to the compost heap, which was covered with 9” of snow. They never got anything from it, but the tracks were really easy to read. Some were even out foraging at stuff sticking up through that 9” snow. Some never went out in it.
In the photo above about 1” of snow fell during the day when they were already out. Since the change was gradual enough, they never bothered to go in. Chickens don’t like change and waking up to a white world is a change.
I think a big part of it is food. If they can forage for food they are a lot more likely to eventually go out that if there is nothing for them to eat. Even then, it usually tales mine two or three days to venture out.
The photo below was also taken many years ago. I always leave the pop door open and let them decide what they want to do. It was +4 degrees Fahrenheit when I took that photo. If a cold wind is blowing mine are not going to be out in it. If they are not in the wind mine usually go out. I have a corner where a solid gate meets the coop, creating a place normally out of the wind. I often see them in that area.
I find that some flocks are bolder than others. Some individual chickens are more adventurous than others. My flock dynamics change in some respects each year as I rotate new chickens in and old chickens out.
Do as you will with yours. I don’t heat my coop, it seldom gets much below zero Fahrenheit here anyway, I know many people have colder weather. And the only time I didn’t open the pop door was after an ice storm where I couldn’t get it opened anyway. I’m not trying to tell anyone what to do with theirs, just mentioning (and showing photos) of what I do with mine.