ah the "High Horse" from play test.
as a cheap horse, there is an additional cost to wander around town (discarding a card) - although sometimes when you are looking for more end of the turn card draw, discarding a card is a good thing.
I see this having a role in both Outlaw and First Peoples plans that focus on holding town square - cheap influence to keep you from losing - maybe extra influence for Mariel or Zac.
or combine with something like a Ranger's Bible for a serious weaponization of influence.