Must depend on the horse. I do think lots of minis are trainable though
Of course they are! Some have even been trained to be service animals.
But a mini is a lot more prone to kick than a horse is. My friends mini bites me every time I swing my leg over his back.
Possibly because having a person your size sitting on him
HURTS. The usual "rule of thumb" for the rider/horse ratio is that the rider plus tack should not weigh more than about 25% of the weight of the horse. Most minis weigh 300 lbs or less, so unless you weigh less than 75 lbs, you probably exceed that, just by yourself. Conformation and condition play into the equation too, but most minis aren't well designed for weight carrying to begin with, or kept in good, athletic condition so that they can carry
any weight comfortably.
Blondie has never kicked anybody - she has never even offered to kick. She is about as close to a Golden Retriever in personality as a horse can get. Even though she's a bit on the larger size for a mini (35"), she is of the more refined type; probably weighs about 225-250 lbs. She's
definitely not built for weight bearing, being roach backed, cow hocked, and prone to locking stifles, but I bought her for her personality. As long as she understands what you want her to do, she is usually happy to do it . . . a little too happy, sometimes - she volunteers behaviors before you can ask.
I think the biggest problem with minis is that people don't take them seriously. They see them as children's toys, or something, and kids are notorious for not knowing what to do or doing things incorrectly when it comes to horses. My 15hh QH Latte spent a couple of years as a lesson pony before I bought her, and evidently, she hated it. She was a greenbroke 4-year-old when they got her, but well enough behaved; within a few months, though, she was nipping and kicking and doing all manner of nasty, snipey things (especially to the kids). She once broke a pair of my glasses, hitting me in the face with her head. So yeah, when I bought her, I already didn't like her very much . . . . but we got through that. Bad habits, once acquired, can take a lot of consistency to break; every once in a while, I catch Latte checking to see if the rules are still the rules. She's just that kind of horse.

The animal I bought was a pain in the neck; in the wrong hands, she could have become truly dangerous. Though she may have her moments, she is a much more pleasant animal to deal with now; I suspect a few folks who used to know her would be astonished to see her doing liberty work with my daughter.