Flocks and individual chickens can have their own likes and dislikes. Some are really bothered by snow and others don't seem to mind it at all. It's the same thing with rain. Cold tolerance can be different, too.
The thing I mainly watch out for are young chickens dealing with new housing or new weather that they aren't used to. Sometimes, when they first come out of the brooder and move into a coop with a ramp, they don't know what a ramp is or how to use it. In that case, you can't count on them getting to water, food or shelter and they may need some help. Sometimes, the first time a heavy rain happens, they take shelter where ever they are and get stranded out in the yard. Often, chickens are afraid of snow the first time they see it and can get stranded out in the yard or run. I can remember some pullets that looked a bit shell shocked when they first saw snow, huddled under a patio table. With adults that are used to the environment, though, mine have always been good about going into the coop to warm up or get out of a heavy wind.
In the teens and 20's, they still go outside a lot. Single digits, they go in to warm up a lot. Once the highs for the day are below zero, like -6 or -8 F, mine usually choose to stay in the coop all day. I know there are other people with chickens that seem to be out more than mine, in the same temperatures. Mine really like their coop, though, since it has a lot of windows and seems to have an airy feel to it. They look out the windows a lot when they're hanging out in the coop. Their food and water is in the coop, also. To me, they seem to putter around in their coop like we do in our houses.
If they had a coop without any light in it, they might not want to go in during the day. Some people have smaller, darker coops, that are mainly only used to roost in. I first started keeping chickens of my own when I was renting an old farm house that already had a hen house. It was a big building that had a lot of windows and the chickens had lots of space to live in it during the winter. My coop designs have tended to be similar to that.
So, a chicken's desire to be in the coop or outdoors, can also be effected by the coop design and the run design. Some runs are more sheltered and comfortable, others are wide open and exposed. My particular run has a cover to block falling snow, but no wind block, other than the coop. The run is on the south side of the coop, but we get swirling winds, as it's in a clearing bordered by woodland. That might also make the coop more attractive for my chickens when it starts getting a lot colder.
