I live in Ohio, snow and cold. I've only had 1 hen (Jersey Giant) go broody last summer. We followed the same path, moving her and the eggs at night to a quiet separate place (our outside mud porch). It is truly a mud porch, so it was a perfect spot. It was nice and hot in summer, so we didn't have to bring them indoors, thankfully. I already have an 80 lb tortoise living in my house and 2 jack russells. Keeping her and the eggs in the coop too chaotic with the other hens laying and wanting nest box time. Plus the hens would lay their eggs by the broody hen and she would grab them and put them under her. By day 2 or 3, we had to mark the eggs and decided we needed to move her for easier food access and calm days in her own nesting box. She was very appreciative, I think, as she was not a very affectionate bird normally and during her brood, she was very engaged with us, eating from our hands. We gave her nice cold yogurt, salmon, trying to give her some protein to keep her strength. Seemed we nursed her so she could sit the eggs. She was a fabulous mom at hatching and took care of the little ones (only 3 hatched out of 7) for several weeks post hatching.