I’ve got five Golden Comets that have a coop to roost in but four of them prefer roosting outside in the run. Everyone I know that has chickens has seen egg production drop during the cold winter months. Ours have put out 5 eggs a day with the exception of a few times it has been in the upper teens at night and we only get 3 or 4 eggs the next day.
It does but thats more a function of the amount of light per day than temperature.
Some people think Im crazy but Im convinced that I maintain better production by bringing them hot water through the cold also. Its true that it stays liquid longer which would help ensure they arent getting dehydrated but I would imagine that the fact that they are warmed from the inside out for part of the day means they dont lose so much trying to keep themselves warm. The waterfowl dont seem to mind eating snow but it does seem to make a difference for chickens.