That's what we understood, but two of our chickens apparently didn't get the memo. We got two eggs on December 21st, the shortest day of the year.
Our six chickens are six different breeds, but they are all alleged to be "cold hardy". All I can remember is that one is a "Buff Orpington" and another is a "Polish Tophat". My wife selected and bought them all, so she knows all the breed names. The Buff lays an egg every day.
The Polish Tophat lays eggs that are supermarket white. Another chicken lays blue eggs. The rest lay brown ones. All of them are tasty as can be.
I'm pretty sure most of the heritage breeds are cold hardy, you just have to watch the bigger combed breeds for frostbite. Other than that, my birds don't mind the cold. It is the heat that they don't like. We string little water misters all over the chicken yard, and they hunker down under those, panting.
We had 25 hens, and during the warmer months we were getting about two dozen eggs a day. We gave some hens to a friend and a couple got eaten by raccoons, but even with 20 hens we were getting way too many eggs to even give away! Now during the coldest months, we usually get three or four a day. They are so much better than store eggs.