What does SH mean on Howrse?

SH on howrse means safe haven
Safe Haven is where you send horses: The Safe Haven is a refuge for all the horses you no longer want or can't sell in the auctions or private sales. It currently has 538949 horses.
Be aware that once you send your horse to the safe haven it is not undo-able! I would only send my horse to SH if it was going to die as howrse keeps it alive!