i do bring them inside, but not for their comfort but mine!
They are chickens, you are not. You would be cold out in the coop, they are not.
I have only had chickens for a few years now, and never used heat in the winter, but want to get some feedback. I have two hens that are in a bad molt right now, They are nearly naked and temps are dropping below zero night and the wind is making the days frigid as well. The water is always kept outside in the pen, but they two hens won't leave the door of the coop. I have moved the water as close to the door as I can but I haven't seen them go out for days now. I have plastic tarps up to stop the wind, but do I also need to heat the pen so they will come out???
Time for my favorite "why there is no need to heat the coop" story. I live in NW Vermont, we are well below freezing at least 3 months of the year, sub 0°F is common in January and February. -15°F is not unusual and we often hit -20°F one or more times in a winter.
My girls' coop is a converted 10x12 horse stall in a really old barn, like 100 years old for that part (150+ for the main part). I built a recirculating heated water loop connected to 5 nipples in a 3/4" pipe into the insulated bottom of the nest box inside the coop. ONLY the pins stick out the bottom. Worked great for a year, then the night before Thanksgiving 3 of the 5 nipples failed. I never figured out why. But to replace them I needed to take the nest box apart. Yes, design flaw!! No time to do that so I put the 1 gallon waterer under a heat lamp in the next stall over. On the coldest days only the 1/4 of the ring on the lamp side stayed liquid.
What does this have to do with NOT heating the chickens? NOT ONE hen EVER spent any time near that heat lamp EVER other than to drink. Additionally one of them decided her first adult moult shouldn't start in the fall as would be expected but the last week of January. The COLDEST part of the year. Half naked hen, if she couldn't keep herself warm, she would hang by the heat lamp right? Well she NEVER did and she started laying again 2 months later. On really cold days the girls make "day nests" out in the dirt and shavings floor barn alley which is their indoor run.
As to some breeds not being able to handle cold - pshaw. I had 2 Cubalayas, developed in Cuba. Not a place that gets real cold. Also 2 Anconas, a Mediterranean breed, again not a cold spot. They never behaved any differently than the other hens including the "cold hardy" Faverolles and Partridge Chanteclers. Yes they were twice their normal size because they puffed out their feathers to trap air, that is how chickens stay warm.
To the OP, tell your mother to research this site and find the stories of coop fires from heat lamps and BBQed chickens that were the result (not to mention no longer having a coop).
As for winter water, I fixed the circulating waterer the following spring, it has been fine for 4 years. You can also use a heated dog water dish, again works fine. They aren't expensive.
