Have a quick release for the seat. Bring it inside and keep warm. Reattach in the morning.
This reminds me of the story my friend told me. On his winter break, he would stay with his grandparents in rural New Hampshire. They had an outhouse rather than an indoor toilet. The seats were kept above the fireplace inside. He would take one of the seats (I don't know why there were two) off the wall and carry it out to the outhouse. He said it was actually a fond memory.