The reason chickens don't lay as many eggs during the winter is not because it's cold. It's more so because of the lack of daylight. If you want to increase your egg production through the winter months, put a light bulb in your hen house (safely out of chicken-reach) and set it on a timer that turns it on to increase their "daylight" to 12 hours.
Ours is set to come on at 5am and turn off at 7:30am, which is about what time we let them out in the morning. We opted to have the light on in the morning rather than in the evening because we didn't want to discourage them from naturally going into the hen house at dusk (and thereby finding other places to roost, since they free range a lot).
We have a very large hen house and have found that a single 75 watt bulb is sufficient. While not all of our hens are laying with this method, we are getting about twice as many eggs with the light than we were without.