I also carry a bothy in winter months, and used it once on a summit in a blizzard. I always carry a small insulated pad, and sat on that (no groundsheet). It was not a great experience: cramped, humid, noisy. But it was VERY cold and windy with driving snow on the summit, so life in the bothy was most definitely better than outside.
The worst part was the condensation dripping all over me - it was like my own personal rain shower!