I thought I read below a certain temp (40-45*?) that all their energy goes into staying warm and no longer producing eggs. If you can keep them warmer than those temps they lay, if not, no eggs!
While most commercial egg farms keep their layers in climate controlled buildings, for the small flock holder, temperature has almost no effect on egg laying. Extreme heat and extreme cold cause stress. Stress affects ovulation. A couple years ago, I kept a spreadsheet for the entire winter. It tracked daily egg production from 4 flocks of chickens. It also had daily weather: daily high and daily low temps as well as precipitation (snow and rain daily totals).
There can be a cold snap yet when ovulation occurred 24 hours earlier, an egg will still be laid. But if temperature affected production in any significant manner and you draw graphs from the weather and production data, long term you would see a trend. There was zero correlation between temperature and egg production. This included periods well below zero F.
Closed up, dark coops are the worst thing one can have. First of all, lots of fresh air is more important than food and water - as important as those are.
Secondly, light, and more importantly, daily light period in relation to dark period (decreasing vs. increasing) is the most important determinant on production. As light increases vs. dark, hormones encouraging ovulation increase. As days shorten, molt often happens and production usually decreases. So winter is when some find a dearth of eggs. But it isn't the cold. Winter coincidentally is when days are short. If one lives in a warm climate, egg production will still go down when days get short.
I also don't ascribe to the notion that one must keep drafts off of chickens. They descend from jungle fowl that don't live in buildings. They can live in trees. How do you keep a draft out of a tree?
The last coops I built, a complex of 5 breeding units, has huge windows (about 1/3 of the wall) on both east and west walls at roost height. The cold winter wind blows right through the buildings. It has been like that for years and I never get even a sniffle, let alone loss of production or death.
The commentary on cold and drafts applies to "normal" chickens. If one has very fragile and non-cold hardy breeds, that is a different story.