How do you keep chickens from getting bored in winter? One way is to give them room or possibly improve the quality of the room they have. I don't believe it's boredom, but shoehorning them into a tiny space sometimes leads to behavioral problems like cannibalism or physical assault. How would you feel if someone were in your personal space all the time? What you describe could be because of lack of space. That's why how many hens you have and how much space are important information. Some idea of what the coop looks like can help. We love photos. The more we know about your situation and what you have to work with the more likely we can offer suggestions that actually apply to your situation.
One way to improve the quality of the space you do have is to give them things to hide under, behind, or above. It often helps a lot if they can get out of line of sight of each other. If your coop is pretty small you may not have much flexibility to do this.
I assume the only time this happens is when they are trapped in that coop for a period of time. They often don't like snow, at least for a few days. They don't like change and waking up to a white word is a big change. When that happens to mine they usually won't leave the coop for a couple of days. Mine forage as I have a lot of room outside that stays in vegetation, some sticking through the snow. So they have a reason to go out. If all yours have is a barren run they may not have that much incentive to go out in that strange white stuff. Shoveling might be an option to get them out. Or you can try scattering bedding on top of the snow. I think it helps if you use the same bedding they are used to. A strange bedding might be as foreign to them as snow.
You can try to distract them with food. They are not going to eat all the time, their crops only hold so much. Plus you still want treats to be a minor part of their diet. Most of what they eat should still be their chicken feed. Depending on what kind of bedding you use, it might be effective to scatter something they have to scratch for. They seem to like scratching.
Another issue in winter is that they don't like a cold wind. It's not just snow that keeps them in. Mine go outside even at zero Fahrenheit as long as it is pretty calm, cold doesn't bother them. You don't necessarily have to have windbreaks all around your run, though that's not a bad thing as long as they have enough openings up high for ventilation. Providing some wind breaks can make a big difference in them wanting to go outside. Mine often go to a corner formed by the coop and a wooden gate to get out of the wind.
Snow will blow in from the sides, not just from straight above. The best way to improve the quality of your space is to provide a snow-free area protected from wind in the run that they can get to.
I'm doing some guessing as to what might be your problem, it could be something else. I don't know what your coop and run look like, it may be real challenging to do much of this. But what you describe is often the result of them being too crowded.
Good luck!
