yes. chickens do sleep better with the light off. Just like all other vertebrates, chickens have circadian rhythms that are regulated by light cycles, leaving lights on all the time will result in messing up their circadian rhythms (they will be up at random hours). You are probably right about the light triggering them to lay more. Increased light duration is on of the cues that vertebrates use to tell them the season. So even though it is really cold out, the fact that you have the light on for more than 10 hours is telling the birds that it is not really winter. In my previous research facility we switched the light cycle from 12 Light/12 dark to 14 light/10 dark in order to trick our mice into breeding more. (14/10 is also what we use in our zebrafish facility to get the fish to lay more)

Great data on the light/dark cycle of various animals! I probably should hunt down what the actual numbers are for chickens.