When I was in high school, I sometimes taught at the children's horse camps at a stable near to my home in exchange for lessons from one of the resident instructors. The stable had a herd of lesson horses, which lived in a big field behind the main barn. They were mostly on the elderly side, and one of them, Patches, was the stalwart seen-it-all, done-it-all old gelding that most lesson stables keep around to teach the youngest kids to ride. He was gentle, tolerant, and completely bombproof.
However, ol' Patches had apparently been a stallion up until he was around six years old (goodness knows why, he wasn't anything particularly special in the way of conformation, talent or bloodlines, but I digress). If you geld a horse after a certain age, they'll often retain certain stud behaviors, even in the absence of a testosterone source. Now Patches had been separated from his testosterone sources at least 16 years prior, but somewhere in the dim recesses of his memory he knew he was supposed to be interested in mares. His way of expressing this interest was to maintain a small harem of mares, which he jealously guarded from the other geldings in the herd (none of whom could have possibly cared less), but seemed to have no idea what to do with them (which was probably a good thing. The mares were all old and would probably not have approved). You'd often see him in the field, hanging out with his girls, looking as though he knew he was missing something, but what? What was he forgetting?