I think one time she tripped over a rock or something and I gave her a treat to make her feel better. Then she did it again and I evidently rewarded her. I started calling it play dead, and she just caught on to it. I don't even know how chickens trip, but she did.
What I would do is they usually have heat lamps at your local feed store and depending on the size of your coop you could have two. I have a big coop and I usually use two heat lamp near their roost. They will huddle up together and stay warm. I don't think I would try the reptile lamp though.
I used to have a chicken that would lay on her side and play dead on command. We recently lost her to a coyote massacre, but good luck with training yours!
I live around a place with those predators, I still free range them during the day and they go back in the coop at night. We also have lots of trees for shelter from Hawks. We do have a chicken run and we use chicken wire and it goes about 2 ft under ground, goes up the sides, and we use it as a...
Temperature: Heat lamps work in the cold and I personally make sure there is lots of shade on the coop in the heat. Also in one end of their run I put light misters up, they seem to enjoy the light amount of water, but not too much and too strong. I also use a water bowl that refills itself, so...