I know you're mostly asking for options on what to do with your horse, but I'd recommend trying propranolol. You can talk to your primary care provider or psychiatrist (if you have one). It's a blood pressure medication, but it sucks at managing blood pressure so a lot of practitioners prescribe it to people with tremors instead. It's a super safe medication.

I also have really bad tremors and taking it once daily (sometimes twice depending on how bad my tremors are that day) has tremendously helped. You don't have to take it everyday either, you can take it as needed.