Frozen eggs?!! Good gracious. Being the huge weather wimp that I am, I'm probably not the best person to ask. If it was me, I would install baseboard heaters, a hot water drinking fountain, and heating pads in the nest boxes. Then I'd make chicken parkas and booties and comb-warmers. There would also be a hot buffet with soup, oatmeal, venison and pie. (And then my husband would ship me off to the looney bin!)
I don't think there's anything wrong with keeping them inside all day. That's some serious cold you're experiencing, and frostbite has got to be a concern. If it's dark for them inside, you might lose egg production, so maybe adding some artificial light could help that. If you're really worried, hang a red heat lamp from the rafters. We used to do this during foaling and it really helped. (Well, at least for low 20s.)
Can you eat eggs once they've been frozen? Wonder what happens if you put one in the microwave.....