Hmmh! That's a good question. I hadn't thought of it.
Chickens probably don't need greens in winter, but they would surely appreciate them. We have a little green house, which we discontinued using because it was too much work to keep it watered and taken care of.
When I was a kid, our chickens didn't get any greens in winter, other than vegetable scraps from the kitchen (outer leaves of lettuce, etc.). As an adult, we only had chickens twice. They only lasted for a few weeks before predators got them.
We got chickens again, last spring, and built them predator-proof enclosures (one for summer, one for winter).
Maybe I can talk my husband into growing some winter-greens for the chickens in the neglected greenhouse. He'll probably bulk at the problem to keep anything watered in freezing temperatures.
You could try growing something on the window sill. Other than that, buy lots of lettuce and share it with your chickens. (Make sure to wash it. You don't want to feed your chickens pesticides.)