You have to start with finding out what the horse's FIRST RESPONSE is the things that surprise or scare him. Spin and run, Shy sideways, Lift head and look harder, Lock up the legs and stand.
This response is what will happen if you are out driving or riding that animal. You can't train that AUTOMATIC, INSTINCTIVE response to fear or surprise. Horse just does it regardless of his training, if he is that frightened.
A horse who won't listen to you on the leadrope, holding the reins, does their Fear Response anyway, to get away from what scares them is NOT DRIVING material.
You can train until horse is aged, he still will respond with his first instinct if he is that scared. You don't want to be in a vehicle behind that spin and run horse, or the one that shys violently if frightened.
I don't care what the breed is, you have to work with each animal and find out their "First Response" to fearful things, before choosing it as a Driving Prospect. TBs are not common Driving horses anymore, because so many have poor First Response instincts. They also move AMAZINGLY fast when fear strikes, some lose their brain as they run away.
I know a lot of folks who wanted to drive TBs, worked with prospects from foal to ages to start driving them. They were experienced trainers, many skills, but even then their prospect TB didn't make a Driving horse. Fear response was poor in bad situations, often ran away when surprised. Left vehicles broken, people hurt in the aftermath.
I would not rule out Driving a Half-Bred TB depending on what the other half of cross was. Quite a number of successful Half-Breds in Driving. The other half seems to give more "think instead of RUN" to their brain.
You will hear stories of TBs being driven, listen to the background of the stories. Did those folks really DO ANYTHING with the horse in competition, or just drive the home farm, etc? How long did they put into training, before hitching and going? Were they driving Pairs or Singles? All these things can make a difference in success in using a TB like you want to use one. One person I know SWEARS that TBs are the best Driving horses. Her's drove!! She leaves out that he was aged and lame in about every leg most of the time, since he was a rescue horse. She didn't drive often beyond a walk, and she took a couple YEARS to work with him almost DAILY, before she ever hitched!! I think she attended one show, not sure if she got into the ring. Did her driving on dirt trails, local to her boarding places. Horse did have some "incidents" while driving resulting in broken equipment. Not what I would call a huge success as a Driving TB. Horse was older, came with a lot of "issues", so her driving times were limited. She only drove the ONE TB, yet tells folks "There is nothing hard about training a TB to drive!! I did it." When he died she got a different breed of horse and it didn't drive at all!
A TB would not be my Driving breed of choice if I were starting out. Just not their best way of being used. They are bred now mostly for speed at the Track. Horse parent combinations are chosen to have fast foals. Nothing is considered about kindly disposition or brains in breeding choices. This is unlike other breeds that are used for other jobs, need those brains, accepting attitude to make nice animals to own.
If you are a beginner, please look around for an already trained Driving animal and take lessons in the Driving, plus hitching and managing situations you will meet on the public road. Get secure in your Driving skills with that Trainer and calm horse, so you can then do things correcty when alone at home or shows.
As you progress in skills, knowledge, you can move to a more exciting horse if you wish. Driving is supposed to be FUN, relaxing to do. Should not be "edge of control" when you hitch and go out. A made horse is easier to start with, learn, then get the fancier animal if you want more excitement in your life.