I remember years ago when they first started breeding miniature horses and they cost a bundle. There were a lot of horrible genetic results but eventually they ended up with pretty decent minis that look like a true miniature of a horse and not just another pony. I watched a horse parade recently and there were tons of minis there. There was only one grouping that were the distorted body shapes, twisted legs and even faces that many of the original minis were born with-obviously not the kind of breeding that should be encouraged!
Now, unfortunately now I see a lot of minis out there that are dumped for very cheap prices or sent off to an auction. I suspect that non-horse people buy them as pets and they end up becoming unmanageable and/or hurting a kid. The biggest thing to know about minis is to remember that they are a horse and treat them as such. Teach them manners and work with them and they are a lot of fun.
You can trick train them and/or drive them and join one of the Miniature Horse Clubs for showing and information. One thing that bothers me a lot is the number of people I see putting their great big kids on one of these little guys.
They simply aren't constructed for heavy riding but people don't seem to realize that there is a difference between a stout pony and a mini horse.
Minis obviously need a lot less food than a full sized horse but every other expense is about the same. They are pretty easy to transport too-I've seen people take the seats out of their mini-vans, cover the floor with rubber mats and haul their minis back there. Of course you have to build a little portable ramp and teach them to use it too.
If you are on Facebook, check out the Gentle Carousel Miniature Therapy Horses page. They have some of the highest quality minis I've ever seen and they take them into hospitals all over the world to visit patients.