Reserpine. (“reh - SIR - peen” is the correct pronunciation. But you will hear everything, even from vets.)
The ‘chill’ drug. Doesn’t make them drowsy, just calm. Long-lasting. Re temperament, can ride normally on this drug.
It’s cheap and easy to administer. Dosage may be once a week, or once a month after it’s started.
Reserpine is a calmer par excellance. In my experience, most vets will prescribe it if asked.
There are some cautions that a handful of horses react badly, but not life-threatening. Most respond well.
Illegal in USEF showing. Takes around 28 days to clear the system. Just to be aware if you plan to show.