This is just my .02, and I am not a professional, but I DO like to drive my horses in some touchy situations (just take a trip to the beach on a major tourist weekend w/kites, rude dogs, children, flapping flags, water to cross and backfiring cars, etc. you will know what I am talking about and this is all likely to happen in a time frame of just an hours' drive)
I take my weanlings around everything I can imagine. Show training and the clipping/blanketing does serve a certain bit of my purpose to desensitize. If I didn't have them from weanlings, then they just take walks with me around all manner of things. Traffic and the "public" are important so the horse learns to trust you in every situation. We do not wrap our horses in cotton and keep them isolated. They live with my sons riding their ATVs in the pasture, we light fireworks around them and we play with RC cars in the pasture, etc. etc. they learn to get used to it and that they will not be killed and eaten, and we are there to protect and comfort them.
When they learn to drive, it is time and repetition that are your friend. Make sure your horse has spent many many hours with your horse in every situation you can imagine. Talk to them and let them know that your voice is an extension of your hands and soothe them. You will be able to see their body language and whether or not they are relaxing and trusting you.
I think ground driving (even w/the cart following) around a lot of situations will help your horse learn to trust you as you cannot truly desensitize for EVERY eventuality. Somewhere, something will happen that you just never could have anticipated and you will need your horse to listen to you and trust you to help him or her through it.
Best advice I have sorry it's not more or better, but I am just an amateur at this, myself.
Liz M.