Jane pushed me in the direction of this thread....
So anyway,
do you want to do breed ring driving or CDE?
Breed show driving is usually done with AMHA or AMHR. Harness is fine harness, check, blinders, 'fancy'. Usually with no breeching, though I do not recommend getting a harness without it. Cart is usually a show cart--Jerald, Houghton, etc...single seat and painted.
CDE driving is done with all breeds and sizes of horses. To enter a CDE with a mini division(properly called a VSE--very small equine--division), your horse has to be under 39" at the withers(or else its a pony and can enter in ponies). There are four levels of driving in the sport--Training, Preliminary, Intermediate, and Advanced(though minis/VSEs can only do Training, Prelim, and Int right now).
A CDE is a Combined Driving Event. It consists of three events: dressage, marathon, and cones. Dressage: obedience, harmony, memorization, training; Marathon is a distance course(4-10k for minis) at a constant rate(come in at a certain time) with hazards throughout. A hazard is a timed(except at Training) obstacle with lettered gates and sometimes 'scary stuff'. Cones is a short timed course where you drive through numbered sets of traffic cones with tennis balls on top. You can have 'balls down' or time penalties(too slow).
It is a lot of fun! For a CDE harness, it must be functional, safe, fit well, have breeching, no overcheck(preferably no sidecheck, which are only allowed at Training), have a noseband. The bit is not allowed to be twisted, wire, or a chain bit. No hackmores or bitless bridles. You may have blinders or not. The cart should be functional, safe, balanced properly, fit your horse, and have a basket(unlike the Hyperbike) for Dressage and Cones. You might be able to(depending on who is judging) do marathon with the Hyberbike. It is preferable to use metal wheels(ie steel/aluminum) or wood wheels--the pnematic tires are usually spoked, and so, are easy to bend or break if you aren't careful. Plus, they can go flat. Dressage and Cones(has to be the same vehicle here), you usually use the dressy vehicle, and Marathon you use a less dressy cart(ie one that can get dirty).
A good site for minis in CDEs:
Mini Horses in CDEs