I have had the same problem! I have a heat lamp in my coop and one of the chickens knocked it down and burned a whole in the coop! I was lucky there was not a fire with the coop so close to the house!
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we have been consistently cold, and what I am seeing is a loss of egg production, but my birds are getting used to it, they are outside strutting around in pretty darn cold weather. I don't add light or heat.
I caution you on a tightly closed coop, the moisture will build up fast, and that is where you will get frost bite. Instead of adding heat, add feed and make sure they go to bed with a full crop. A lamp, an extension cord, high wind and water and snow, are a darn good recipe for a fire if you ask me.
Mrs K