My coop is running around zero degrees fahrenheit, give or take 10-20 degrees. If I don't harvest the eggs within a couple hours of being laid, they do freeze. As long as the shells are intact, it doesn't seem to hurt them, but I'm finding that quite often, the shells split and crack when they freeze. Water expands when it freezes, and since the contents are mostly water, there's a good chance the shells might crack from the pressure. The other thing I've noticed is that sometimes when they've frozen, the yolks gel and aren't runny when they thaw out. They still work as hard boiled eggs, but if you like your fried eggs with hard whites and runny yolks, they won't work for that, and they don't scramble well.
The cracked ones I boil and chop, shells and all, and feed back to the chickens. They love it.
Some of them remain intact, even though they're pretty cold. Don't know if it's because I caught them early enough, or because they just have somewhat more flexible shells.