She was Machan Li's daughter, but was traded to Horse in exchange for various power-ups. She wasn't "Horse's Guy" (that would be Pho), but Horse has been using her as a mastermind to work up plans for bringing him into the Cycle.
Cai Wen still owes Horse some country-tagging plans in exchange for formally freeing her from his service, and the understanding is that she can still think up plans for him. (3 plans were promised, and 1 was used for Wolf's Talisman, and 1 was used for Xian's minirun for Horse)
When she was traded to Horse, her name was part of the deal (as it would have been a connection to her father). Cai Wen proposed the name "Mystique", which she likes well enough.