There is indeed a single ending (so far) where you wind up a cute jenny instead of a handsome jack, and it involves being incredibly uninteresting to someone around the outskirts of the farm.
Low meaning less; the donkey behaviors boost a number that I generally refer to as donkey brain; when that number reaches certain thresholds, that's what triggers the different texts, behaviors, and endings. To start this specific scene, you want to go to the Edge of the Farm basically right after running from Faye in the farmhouse, then wait in the Crossing the Wheat scene for the event there to start.