I am going to explain a few things here and they will clear up some confusion about light, winter and laying.
I provide 12 hours of light for my girls, because during winter, they are not in their summer coop, but in their winter condo inside a heated garage. Garage just has a window that does not really provide sufficient light. I also keep pigeons alongside my chickens. I don't want them to go NUTTY , due to darkness. My chickens have, at all time.... FOOD AND WATER. available. The egg production drops off significantly during the colder winter. The heating of the garage is only to just above freezing temps.
Now for the egg laying cycle.. A chicken in full production mode will lay an egg each day. It occurs in most cases every 25 hours. ( no need to correct me that yours do it at different intervals,there are exceptions everywhere. ) A chicken lays eggs during daylight. ( again there are those that laid eggs at night that dropped from the roost and broke below them,) Lets start a chicken laying on day 1 at 9 AM. Next day should be about 10 AM. For practical purposes, lets say there are 8 hours of daylight during the shortest days of winter. ( I'm skipping the twilight at dawn and dusk,) This means that for 8 days your chicken will lay daily. On day 9, it gets dark so chicken waits until next morning to lay her egg. This mathematically translates to 3 to 4 skipped laying days per month.
Ok, now you are thinking,,,,,,,,,, WO WO WO, MR. CAVEMAN...... According to you I should not have much of a drop off in egg production due to less daylight. I did not say that.
Added amount of light time, means that the chickens will be eating during that period. REMEMBER THIS. In order for eggs to come out of chicken, food has to go into chicken.
I do not think it matters MUCH whether you add the light in the evening or morning. It may and you can experiment which way is better for your chickens. Another thing to consider is the intensity of the light. If it is quite dim, then it will have less effect than bright light similar in value to daylight. Battery hens at egg production farms have lights on 24 hours. That does not mean that they do not sleep at all. They snooze whenever they desire.
Bottom line..... There are multiple factors to decreased egg production during winter. Adding light is good but not the SILVER BULLET.