This last winter was my first winter with chickens. I had 7 birds roosting in a 3x3x3.5 simple wooden structure and free ranging during the day. I only had 3 girls when I built it, the other 4 came just as winter hit. I'm no carpenter either- It was super drafty, a little lopsided, and was just made of basic 4x8 pieces of particle board, shingled roof, and 3" rounded posts for roosting bars. I used pine bedding inside. That winter was -20 or so at night and 10 during the day, which is much harsher than usual here. We had a foot of snow frozen solid on the ground. Not much compared to many states, but in the desert of SW Idaho that's pretty bad. In the mornings when I would go to check on the girls, their coop would be warmer than my house! 7 little bodies steaming up that little box! Honestly, they're wearing their own little insulated jackets. Birds in the wild, like pheasants, sleep right out in the elements with very little shelter. The chickens can handle a little cold. And I only had freezing problems when I left eggs over night. I just made sure to check for them periodically throughout the day.
Perhaps if egg freezing is a very bothersome problem, don't encourage them to lay in the winter. Let them rest and continue again in spring.