based on how much you charge by the month, just divide that to hourly rates.
So, if you charge $650 a month, then your rate would be $30 an hour.
I'd tack on a travel fee. 10 miles is 20 miles round trip and you're making it easy on the owner by them having the convenience of not boarding the horse or having to trailer out. You're also taking the time to drive 10 miles out and 10 miles back. Wear and tear on your car, too.
It's a business. Treat it like one and charge a rate that you feel comfortable working for.
So...let's use the $30 an hour rate....I'd say $1 a mile one way, so $40 an hour.
Doesn't matter if the horse has big issues or small ones....your time is what matters.
If you live in a low income area and this person is also low income, you may have to adjust your rates to reflect that.
For example, I know areas where trainers cost $10 an hour. And higher income areas where trainers charge $75 an hour.
Of course, your experience will mean a lot, too. So, low income but you're truly a good trainer, know what you're doing and can set up a workable lesson plan....at least $25 an hour, if not, $30 an hour.