No. I only use a light when I want to increase daylight hours. I actually just stopped that this week, as the days are getting longer. Last night, though, the moon was so bright and shone right into the coop windows (there are four large ones facing south), it must have seemed like day all night. I wonder if I will have more eggs today than usual?
I use a night light on a separate timer so it goes off 15-30 minutes after the main lights which are also on a timer. My main lights are set to go off right after sunset. Since my chickens like to stay out until the last possible minute and do so, the main coop light draws them it as night sets in. They load up on feed and hop onto the roosts. The night light accommodates any slow/late movers in the coop before it goes completely dark.
I wish mine were asleep right away. I can go out after dark and several are looking out the window at me!!!
I use a solar powered light kit. It was about $30 at Lowes and came with a solar panel and three spot style lights. I have two inside the coop and one outside pointing towards the coop door. It provides a very subtle light in the coop. I've had a very small reduction in egg production over the winter compared with a few people I know locally who have seen their egg production all but stop.
Yeah...I do use a small nightlight in mine. I've read that it helps as a predator deterrant. But mostly I use it so that if a chicken wanted some water, she could see just enough to get down and get a drink. It's also just light enough for me to (dimly) see what's going on in the coop (through the windows...with binoculars from my bedroom window...lol).