Poor little thing. He could do with some worming as a precaution and feeding. He might also appreciate a blanket. He is probably not coping well with the winter, coming from Florida. What is he doing with such a huge saddle on him? I am not sure that minis should actually be ridden, and certainly not with that saddle. It will do damage to his kidneys and there are few muscles in any horse's loins, but he has none at all.
I would also get a harness maker/fitter to come and check that the harness actually fits him.
The cart needs to be as light weight as possible. The shaft should be the height of his shoulder point and should come no further forward.
When the harness is properly fitted you can start ground driving, first with the traces knotted and pulling nothing. Practise turning, stopping, starting and listening to your voice aids and the whip on his shoulder. He should never be hit with it. It is more a guide, but never drive without a whip. It could be a life saver.
You need to drive with your left hand and contrary to what they do in cowboy films you should not slap the reins on his rump. The long reins will also cause a lot more pressure on the bit than the riding bridle. To get an idea what it feels like for the pony stand holding the bridle with the bit against your bare shin bone and have someone hold and pull the reins (do the curb chain up around your leg if there is one!) It can hurt! This should give you some idea why you need to be sympathetic with your hands.
What you should do when starting is to shorten the reins gently which gives the pony the idea that he is about to be asked to do something different and then ask him verbally to walk on.
Once he is happy with moving off in front of you and is responding to your voice and reins and whip, enlist the help of a couple of friends and get them to hang on the traces as if they are the cart. They need to try to keep the weight even and allow the pony to pull them as you give the commands.
Then, take the cart, put the shafts into the round tugs on the saddle but do not do up the breeching or traces. If there is a panic you need to be able to release him quickly. Have another person hold the cart to keep up with him. This is when it could get interesting. He needs to be reasonably happy with the sound of the cart bumping along behind him, and the sound of the wheels. You need to drive him at first in straight lines, then try turns - big arcing turns. Turning with a cart, because of the rigidity of the shafts can be a bit scary and difficult for a horse or pony who will have to learn to do a sort of side step in order to turn. Do not pull too much on the left or right rein as the horse or pony could get his neck injured on the shaft.
Once he is alright with all the above you can do up the traces to the cart and the breeching. Have someone lead him for a few minutes and walk along with the cart yourself. After a few turns round the field the leader can let him go but walk along with him and you can get in the cart, but be prepared to make a quick exit should things go wrong.
Practise starting, stopping, turning etc and once he can do all these things you should be good to go. When you do venture out on the roads, you would do well to get your leader to go with you to reassure him if he gets a bit worried. And you would do well to keep a set on "L" plates on the cart so that drivers will know to give him a wide berth!
Keep going back to practise in the fields and set up cones or something fairly light weight to practise your accuracy on turning and driving straight.
Because he is so small, do not overload the cart and you do not say if you have breast collar or full collar, but he would be much happier in the breast collar as it is less likely to restrict his breathing.