If it helps, my brahma stopped laying completely by mid October, they had been laying like champs up until that point. And mid October is not cold (by normal people standards) here, so I can't say that the cold played a role for them
I think it does, to a degree. The main factor is light for sure, but especially for birds that can't handle the cold, it does play a role. When the cold weather hit for good, my serama, who were laying one to two eggs a week, stopped completely