I've been thinking about growing greens to feed the chickens over the winter, too, but not so much because I want to "spoil them."
One reason I have chickens is so I can get healthy eggs to eat. The more greens the chickens eat, the higher the beta carotene (and deep orangy-yellow color of yolks) content of the eggs. For this reason, I also add flax seed to their feed.
Even if your chickens seem "picky" it's quite possible that if the only option they have for greens are the frozen ones you offer them, they will gobble them up. I've noticed my hens ignore something that I try to give them, but then hours later when they don't find anything more desirable, they start eating.
Anything that is quick growing should be good to grow over the winter under grow lights or in a greenhouse. I have some winter rye that I didn't end up using for cover cropping that I think I will try growing this year. It will germinate in temps as low as 30 degrees F.
I have some growing flats, but I'd rather use them for seed starting for my garden. So, I've saved a few of the half-gallon containers in which orange juice and some milk products are packaged. When they're empty, I rinsed them out well, then cut them in half along their long side. I'll use these as growing "flats."
For now, there are still enough green things growing. I keep pulling up dandelion greens from around the fenceline for the "girls" and they keep inhaling them!