OP: I agree to try peppermints - you can probably find something very small (like Tic Tacs?) that might be just enough for a mini.
If a horse doesn't consider food a 'reward' then I would try other ways to reward like petting or scratching. But, clicker training and food as a reinforcer is a great way to train certain things. I think you can over-do the treating so you have to watch and see how it goes (my TB mare will not leave you alone if you give her a peppermint, so I tend not to give her any).
Our mini, though, was a mostly unhandled broodmare before we got her (she's 22 now and we got her last year). She is just very timid and shy, and that may never change. She does like food, though, so it is possible to give her little rewards for allowing us to "catch" and halter her (something she is reluctant to do). So far she hasn't turned into a biting maniac.