I don't heat my coop, nor is it insulated and I don't use supplemental lighting to encourage egg production. Yes, my egg production is down from earlier levels, but I have come to understand that these are living creatures with a naturally built in timetable for doing things, not Pez dispensers for eggs, so I don't care about the eggs. I figure if they have a natural slowdown period, it's there for a reason and who am I to tamper with that? My main goal is to them through the winter months with a minimum of stress and have them come out in the spring strong and healthy. If I've done that, they'll reward me with decent eggs then. I have 21 birds out there and average 9-11 eggs a day, and those are coming from the pullets that will often lay during the winter of their first year. Now, that's me and what works for me - I well realize that everyone is different, with different goals and circumstances from mine, and that's just fine. Mine have a large, plastic covered run and their pop door is open 24/7, so even during sub-zero weather, high winds and snow blowing sideways, they only use the coop for roosting and laying......the rest of the time they are out in their run.
That said, it does seem like your production dropped off rather abruptly. @aart is spot on about the food. I also feed All Flock or Flock Maintenance to my chickens for the exact reasons she outlined. They get plenty of oyster shell in a separate container and take what they need out of it. I also use up older eggs by hard boiling them, crushing them shells and all, and feeding them to the girls. They love it, it's a protein and calcium boost, and since I just toss that on the floor of their run they get plenty of exercise scratching in there for any little tidbits they may have missed. I don't worry about that causing egg eating - the crushed up cooked eggs they get bear no resemblance to what they lay as far as they're concerned. So in the case of the egg that they were pecking on, it's possible that it froze, cracked, and that's why they went for it. You could stir around in the nest material to see if there's any signs that that's been happening regularly, though. The straw or whatever you have in there might be damp, there might be chips of eggshell, some sign that they are actually eating eggs regularly. I just don't think it sounds like that.
If it was me, I'd keep feeding them well and let them rest up a bit. Good luck!