I had a white heat lamp on for 24 hrs/day for a week or so when it first started getting cold. It didn't affect the quantity of eggs but it affected the timing quite a bit. Before the light mine would always lay in the mid-morning, right after lunch I would collect eggs and that'd be it for the day (3-4/day).
After a day or two of the white heat lamp being on, when I let them out in the morning (8am or so) there would always be 3 eggs ready for me to take. They started laying at night! After a few days I figured I musta messed up their little internal clocks so I bought a $5 mechanical timer and set it to come on at 6:30am and off at 8:30am, and after a few days they got back on schedule.
At the same time I hooked up a red heat lamp to stay on 24/7, so I have the red lamp on all the time and the white lamp on a timer for 14hrs/day. The red lamp hasn't affected anything as far as egg-laying goes, still the same quantity about the same time every day.
Tonight is our first SUPER cold night, supposed to get down to 5 and the wind is HOWLING.