As someone who has been driving minis and large horses for 20 years, it is my opinion that much of the advice being given here is TOTALLY against good driving practices, regardless whether or not you have a miniature horse. If these practices were done with large horses in public, experienced drivers would have a heyday!
First, you NEVER just lead a horse pulling something, as MiLo Minis has already stated. You can read her reasons above. I will add mine and the rest of the driving horse industry's:
When you are leading a horse without something attached, and it decides to bolt, jump, etc., the horse swings around but you still have their head, because a horse can't leave w/o it's head. When you have something attached, then the horse can't swing very effectively w/o sideways pressure on the wheels, which in turn will dump the cart over. Either that, or because the horse can't swing, it bolts harder in front of the handler. In either case, said cart becomes a weapon for both human and horse.
With the driver in the cart when the horse decides to "leave", it can move sideways in the front because it's head is "free", and the wheels will pivot and take up the sideways motion. If it bolts forward, the driver moves with the cart, therefore hopefully staying with it, and stopping it before it becomes an issue. I know that when I have been in the vehicle of a bolting horse, there is no way that I could keep up with it on foot! Yes, in both situations, a driven horse can still dump the cart, and I have seen that happen. I think there would be more wrecks if those bolting horses were only headed without someone in the cart with reins in hand. American Driving Society has strong concerns about people on foot heading horses, but to have a horse pull a garden cart while leading the horse is not just trying to keep it in one place.
I'm not trying to ruin anyone's fun, but quite the opposite. If you have a wreck with a horse, #1 - You and/or the horse and/or spectators may get hurt, #2 - Your horse may never drive or pull anything again. Case in point, very early in our learning to drive, we had a QH that we trained to drive. My mom was signed up for a parade, but at the last minute she didn't feel the horse was ready. The people at the barn said, "Oh, it's just nerves, you'll be fine." Wouldn't you know, even before the parade started, the horse went up and down in the shafts, and never drove again. We tried. He just couldn't get over it. None of that sounds like fun.
If nothing else written convinces everyone that this is not a good idea, figure on the lawyers. When there is a wreck, they will look to see what the "experts" do as to whether or not there has been negligence. There is a reason that you can't purchase a garden cart for your horse to pull while only being led. It's not safe, as we have stated. Why on earth would you want to do something with your mini that isn't acceptable to the rest of the driving world?
Katiean, although your vehicle is very cute, it also is not stable, just for the reasons that you stated. It is not cut under (an actual carriage term), meaning that the wheels will hit the box if turned sharp. In the carriage world, this is considered a vehicle to be driven by people with experience. When the wheels hit the box, the rubber will catch the box and jackknife the vehicle, rolling it (almost been there when the horse decided to back up at an inopportune time). Usually, there is an piece of hardware known as a roller bolt that is attached to the box at just the point where the wheel will hit the box. This is to HELP the wheel from not catching the box. If the wheel has a steel tire and not rubber, you use a rub iron instead of a roller bolt. We have a Runabout to which we show our big horse. The carriage show we use this vehicle for has a separate division for not cut under vehicles, known as Country Vehicle. The reason those vehicles are separated from the cut under vehicles is because they are harder to drive sharply. You have to make bigger swings.
The best prevention for accidents is education. At one point, we were novice drivers who depended on others for sound advice. A good driver is one who puts safety first. While the rest of the horse world may critique what colors look good with which horse, the drivers are ADAMANT about safety. We have been showing carriage shows for 10 years, and open and breed shows and parades before that. I can count on one hand the number of shows we have been to that have NOT had a wreck. Most of these wrecks were with very experienced drivers where something went wrong: equipment failure, horse balked, etc. The worst wrecks seem to be with horses that you "would have never have guessed". The biggest wreck I have witnessed at a parade involved a driving team, not ridden horses. Driving is not something that you "play around with" or do because it is "cute". If you jump over to the mini driving forum, there are some good questions being asked there that will help you with your driving skills.
http://www.miniaturehorsetalk.com/index.php?showforum=18
Again, my point is not to make enemies. If I didn't care about you all, I would just scroll on by. Please be safe!
Once you have been driving for any length of time, it's not a matter of if, but when you will have a wreck. I, so far, have gotten by pretty well, only by having small wrecks that haven't resulted in injuries, but have busted the harness and cart!