I've always thought that padding horses was a cruel practice. It's un-natural for TWH to move that way. If they were meant to move that way, they could do it with flat shoes! And don't get me started on the soring practices used in the Big Lick show circuit. I know that not ALL owners in the BL use those practices, but they all do use the pads. That being said, I have had the great honor of knowing two exceptional TWHs in my life, both were padded up. One of which was a celebration champion twice, we always called him Gambler, I'm not sure what his Registered name was, or I'd share it. The other was a horse named Nigger (excuse my french), which we quickly changed to Black Boy. And both stuck out in a barn full of QHs. Both of them were gentle giants and you couldn't ask for a better behaved horse than either of them. They were used at local horse shows in Women's gaited classes after we got them. We went out of our way to make these horses were comfortable, and let them be horses as much as we could. All the kids would hand walk these two and let them graze, we even prepared a small paddock that they could be turned out in to graze and to get out of their stalls. And as soon as the show season was over, their pads came off, not to be put back on until just before the next show season. They were allowed to be horses for the majority of the year, as our show season only lasted from mid to late March through Labor day weekend, with a grand total of 11 shows in between. I wouldn't ride those two horses while they were padded up, but I took care of them. I even ponied them from my barrel horse every once in a while. I done everything that I could to make sure that they were happy and fit.
I hope you find the horse you are looking for and rescue it from a life lived in a stall with pads on it's feet, and from the possibility of being sored as some of the BL owners do. Good luck!!!!