I live in Michigan and it is really cold but my 21 hens are laying 19 -21 eggs a day.  I give them 22% protein feed and daily treats since their yard is covered in snow and the ground is frozen solid.  They are young (first year).   I expected them to drop production during the winter but they didn't. I also give them oyster shell in a separate container.  They have access to feed and oyster shell 24/7.  They absolutely love sunflower meats I get at the feed store.