I have all of three hens, and this is our first winter. New Jersey isn't exactly known for hard winters, but this one os giving it a serious go. Cold
enough for long enough that we had pipes burst in the house from freezing, despite keeping the house heated...
So, my three hens, living in a 4x4 foot coop with run, have been getting through this cold spell just fine, with no supplemental heat. The fact that their
water freezes is an issue. I did put a piece of bubble plastic (an insulated swimming pool cover) over the roof and two sides of the coop to reduce the wind blowing through.
Generally, they don't come out when there's snow on the ground, although the Buff Orpington braved it today. And yeah, frozen eggs definitely happen, but the birds seem to be ok.