Google "lights to keep chickens laying". Lots of good info and much of it here on BYC. Keeping them in production is the only valid reason and when it is done, it is done in the morning.....never at the end of the natural day.
Having said that, my suggestion is don't do it. Unless you are running a commercial flock and need to fill orders for customers, let them slow down and rest for a few months. Let nature run it's course. They will start to pick up again as the days start getting longer. Until then, if you currently have a surplus of eggs, you can freeze them to use in just about anything that does not require a whole intact egg. Use what you do get for anything that does.
As an aside, this deal with winter light has been known for a long time. Long before electric lights were available. Back in the day, before the large commercial layer houses were around, farmers and such (people like us) were the commercial layers. Due to hens shutting down, eggs in winter were scarce. So winter eggs were the valuable eggs.......maybe 3X what they were in spring and summer. So tricks were devised to maximize natural winter lighting to keep them going to the extent possible.
Go back to the 2nd post in this thread and study JackE's Woods house. Notice all the openings on the south side. Those down low and those up high and also the side windows. Both sides.....so window openings on all sides except the north one. Also know that Jack painted the inside of this coop white. So in winter, it is bright white in there and the light starts reflecting around at the crack of dawn. It is not dark as a house with few to no windows would be, or those with windows covered or not facing south, and with dark natural wood inside. It all counts and it all matters. Back in the day they even went so far as to suggest facing the coop about 10 degrees east of south to get the maximum benefit of the sun. And no extension cords or solar lights required.