Chickens have historically lived all over the world for a very long time, including in areas that don't have cold winters. Also, the wild ancestor that domestic chickens came from - the red junglefowl - is a tropical bird that wouldn't have dealt with serious cold neither in the fall, nor in the winter. So I'm not convinced that molting is related to the winter cold at all. Especially because, unlike wild mammals, chickens don't have a different coat for cold weather vs. one for warm weather, like when mammals shed the thin, summer coat to be replaced by a much thicker/longer/warmer winter coat that is often a different color, too, to camouflage better with the winter landscape. The new feathers that grow in on chickens are the same as the ones they just shed, they don't have a separate winter coat, and the new coat lasts them through all seasons until the following year's big molt (some may have minor molting in the spring as well, though not all do). So it looks like it's just a matter of replacing worn feathers, and the timing is... just what it is. Probably diluted by thousands of years of domestication and human-driven selection pressures in other directions.
