Interesting observation regarding bird size. My winter hatched birds are also much larger than my spring hatched birds... In fact i raised a batch of chicks this spring and kept them indoors in dim light and have the smallest birds i 've ever raised. I added light to this coop to try to offset that effect going forward. As for supplemental lighting for eggs.... I do it and it makes a big difference. I do find that it can lead to some feather picking so you need to be looking out for it. I use two 830 lumen LED lights in my 8 x 16 coop (4.5 watts each) plus a .5 watt LED to simulate dawn and dusk. I have the lights on 3 separate timers (overkill) with the . 5 watt light coming on first , then one of the 830 lumen lights for several hours followed by the 2nd light and then reverse the order with the .5 watt bulb going off last . Total time = 14 hrs. I start the lights at 6 am and end at 8 pm. I have two coops and i am letting my older hens rest until jan and then will supplement them.I am in NW Ga and we don't fight temperatures being too low like some of you do. However, I DO use lights, starting in mid-November. I only add light in the AM, never the PM. Light is added and gradually increased such that they get 14 hours of light per day.
Now - my reasoning is slightly different than those offered so far. I have found that LF (I raise Columbian Plymouth Rocks) finish larger if I hatch them in the winter months. I typically set my breeding pens up in late Nov-early Dec and finish my hatching right after New Years. It has made a HUGE difference in the size of my birds once fully grown. Secondarily to this, the birds hatch in winter are much larger when the full blown summer heat sets in and I have lost NONE to heat related issues since I began hatching earlier.
For those of you looking for egg production, lights are going to help tremendously. Egg production is directly related to light.
I've done this for many years and I have yet to see an adverse reaction in my birds. After I am finished hatching I may turn the lights off for a short period, but normally turn them back on so that I can fill orders for hatching eggs in early Spring.
Hope this helps