The reason egg production goes down has nothing to do with the cold. It has to do with day length, most specifically hours of light. Egg farmers will have lights go on automatically in the pre-dawn hours so that their flocks keep laying through the winter. I don't give added light as I feel their bodies need the break.Chickens can tolerate the cold. We have been getting down to -30F for the past few weeks. We have put thick plastic covering surrounding the external walls of our coop. The chickens have adapted, however we are only getting 1/2 the eggs we normally get. We also feed them extra protein - dehydrated worms in the in the months, to help them keep warm. So far, so good. As weather warms up, the egg production normally increases again. (Interestingly, our friends in Guadeloupe, who also have chickens are facing the same problem with diminished egg production as the temperature has gone down more than anticipated. The owners belief this is due to climate change)
As far as chickens and low temperature, you need to understand their physiology. Their normal body temperature is between 105 and 107 degrees F and they don't lose that heat by sweating, like we do. They have a layer of down feathers under their outer feathers. The down traps the heat very well, as you would know if you have ever worn a down coat.