Using a red light in chicken coop?

Does it disturb the chickens to keep a red heating light in their coop when it gets cold? Also, at what temperatures do I need to use the lamp in to make sure they keep producing eggs?

It's not the heat that will lower egg production during winter, it's the shorter daylight days.
If you need them to keep laying during the winter, you will need to add more light.
Some people put a light on a timer to come on 2 hrs before sunrise and/or 2 hrs after sunset.
I, personally, do not provide any extra light since I want to allow my hens the rest and slower egg laying over the winter.
I also do not provide any heat unless I have Seramas outside; in which case I'll provide some heat when necessary for them.

A red "heating light" is a big fire hazard, and really only needed when you have young chicks

For egg production a 40 watt bulb used to add a few hours of light is all you need

Yeah, the heat is not the issue to them laying, the hours of daylight is. When the days start getting shorter they go into molt and stop laying eggs. They use the protein and other nutrients that was going into the eggs to make the feathers.

There is a myth prevalent in this forum that 14 hours is a magic number for daylight hours to keep them laying. That 14 hours comes from what the commercial producers use when they totally control the light. If you live far enough away from the equator that you get much more than 14 hours of daylight during summer, your chickens can start the molt before the days get as short as 14 hours. It's the days getting shorter that causes the molt, not a magic number. Otherwise chickens close enough to the equator that never see 14 hours of daylight would never molt.

I can't tell you how much daylight you really need to keep them laying where you are. But all the light you need is enough so that you can read a newspaper in the coop. The wattage needed can vary depending on how big your coop is.

Putting a heat lamp in a coop CAN be a fire hazard, but no more than a heat lamp in a house. If installed properly, there is no more risk. I used three in my coop, hung at least 18 inches from the floor with double safety (two chains so if one broke the other would hold). If attached securely and correctly, they are fine. Obviously, don't attach them with clips or close to wood or bedding.

Birds can see the red spectrum (unlike some other animals) so the coop will not get totally dark, but the chickens will get used to it. I used florescent lights on timers to simulate daylight and egg production slowed, but did not completely stop.

it is important to add that in my area, temperatures get down to below zero. Last night (October 10/11) was 35 degrees already. I have mostly Serama, which are considered a lighter feathered bird, so this is why I heat. If I had a larger bodied/feathered bird, I wouldn't bother.

Question...does regular 40 watt lighg bulb hurt the chickens eyes, if used 2hr in a.m. and 3 hr p.m. for 5 months of deep winter? Coop is 4 1/2 by 5ft by 5 ft tall.