You’ve hit a few different topics but let’s try to address them one at a time. First, do they need the heat? The short answer is probably “No”. That depends on what your coop looks like.
Now, some discussion. Do you provide heat for the wild birds that overwinter? Of course not, they don’t need it. Neither do your chickens. Your chickens are wearing a down coat, they are perfectly capable of keeping themselves warm. You don’t need to keep the area where they are warm, you need to allow themselves to keep themselves warm. There are two elements to that.
Chickens, like other birds, keep themselves warm by trapping tiny pockets of air in their feathers and down. It’s those trapped air pockets that provide insulation and keep them warm. If they are in a strong enough breeze to ruffle those feathers those tiny air pockets can escape and they lose the insulation effect. They need to be able to get out of strong breezes when they want to. In summer, warmer weather, they like those strong breezes. But when it gets cold, near freezing, mine avoid strong winds. I took this photo when it was 4 degrees above zero Fahrenheit. I left the pop door open and let them decide what they wanted to do. Since a strong breeze was not blowing they went outside.
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Your big danger in freezing weather is frostbite. Any time the temperature is below freezing there is a risk of frostbite, yet your birds that overwinter and my chickens that go out in fairly cold temperatures don’t get it. They can handle really cold temperatures as long as the moisture level is low. Inside a coop you can have a moisture build-up from their breathing, their poop, maybe you have unfrozen water in the coop, or maybe you have some other way for water to get inside. That excess moisture needs to go away. You handle that by having good ventilation. There are different ways to provide good ventilation. Some people pretty much have one wall wide open, covered with wire, but the other three walls are solid and the roost is back in that cul-de-sac where breezes don’t get to them. That’s kind of a specialty design, getting the proportions right, but those are used where it gets colder than you will see. I have openings at the top of my walls so any breezes are over the birds’ heads. You will get some slight air movement where he chickens are but that’s not strong enough to ruffle their feathers, it just gets the moisture out.
If your coop is pretty much airtight so moisture cannot escape they will be in danger of frostbite when the temps get just a little below freezing. People that have experience frostbite problems have solved them by providing more ventilation. That type of passive protection is good insurance, the birds are protected even if you have power outage. You don’t have a fire hazard out there. And it’s economical, you are not paying for electricity to dangerously heat them.
If it is airtight you also run into the problem of possible ammonia poisoning. When the poop breaks down it produces ammonia, which is dangerous to their respiratory system if it builds up. Ammonia is lighter than air so if you don’t have ventilation up high it can build up. It doesn’t take much of a hole up over their heads to let that ammonia out, a lot of out coops aren’t that airtight, but you do need some way for that ammonia to escape.
Now, does the light affect their sleep or egg laying? Chickens need their dark time. You can have behavior problems and egg quality problems with too much light. If you are using a red heat lamp bulb that’s probably not bothering them that much. If you are using a white bulb, well that’s probably not a good thing to do.
Light is pretty important to egg laying. The longer the day the more the hen can eat and digest. It takes a certain amount of nutrients to make an egg, so egg production can drop with shorter days. Also, light is a trigger for when a hen releases a yolk to form an egg. Another trigger is when she lays an egg. They have the timing worked out so a yolk is released when the egg can be laid during the day, not at night when they are on the roost. So shorter days can result in fewer overall eggs being laid, but it does not stop them for laying.
What is more important to egg laying is whether the light is getting shorter or longer as it naturally does with the changes of seasons. When days get shorter in the fall/winter, hens stop laying eggs and molt. A lot of pullets skip this molt their first fall/ winter and keep laying until the following fall/winter, but mature hens will stop laying and molt. The days getting longer in the spring is a trigger for them to start laying again after the molt is over. Some hens, especially production breeds, don’t wait for the days to get longer after the molt finishes but start laying then, even with the days still getting shorter. Each hen is an individual and does these things her own way, but there are trends and tendencies.
If you are providing light and stop it, you have shortened the day so they might molt and stop laying, going back to their natural cycle.
If hens lay or a long stretch, say 13 to 18 months without a break, their bodies kind of get worn down. Egg production drops substantially and the quality of eggs laid can be affected. When they get to that point it’s a good thing to let them molt and not try to keep them producing with light.
So can you provide heat during the winter? Of course you can, they are your birds. Do your chickens need that heat, not if they have a proper coop with breeze protection and good ventilation. Can providing that light at night affect their behavior, probably not if you are using a red light but yes if you are using a white light.