An Instructor can be helpful in sharing knowledge of fitting a cart (a cart is ALWAYS 2-wheeled) for starting out. The cart is usually wider between the wheels, give a bit more stability for starting driver and new-to-driving equines. There is no hinge in the middle, as 4-wheelers have to fold if horse does some unexpected backing or turns suddenly. 4-Wheelers are what you “move up to” after gaining driving skills, confidence with the 2-wheelers.
You usually start out with very light vehicles, but only need it for a very short time before moving to a slightly heavier vehicle. Finding a Trainer for your equine to train it for driving might be a better way to start, then you can watch and learn, participate as you gain skill and knowledge. Trainer is going to spot things, problems, have solutions because of their previous experience, much FASTER than you will as the beginner. Often all horse needs is confidence from handler to get thru certain steps. Other times horse REALLY needs some skilled eyes and hands on the reins to get to the next level of training.
Certainly not impossible or extremely hard to train your own Driving horse, but you need knowledge to keep building on those basics. Horse needs to be rock solid in obedience, each step of the way before you ask for harder steps forward.
Checking with the American Driving Society site, you can find local Driving Clubs in each State, contact people to ask questions, find Trainers, equipment near your area. They are very willing to help if asked. Do wander the site to learn helpful information, see if things are happening in your area in the Omnibus listings.
http://www.americandrivingsociety.org/Your_Region.asp