I have owned and ridden gaited horses for a long time.
Each breed has is't =/-'s. You will not find most TW have a smooth enough ride.
I have mostly ridden Icelandic's (who have the smoothest ride out there) peruvain Paso's. Peruvian paso is a very smooth ride but there are some major health issues with some of the lines. They just can't stay sound and I know many that have to be put down at a young age because of it. So doing one's homework before looking into them would save you a lot of heart ache.
In Icelandic's you have to watch waht is called "sweet itch"... some Imported Icelandic's have this problem.
Very rare,,in the domestic bred ones. Health wise they are one of the most sound breds out there.
Been on my TN walkers and the ones I have been on..are only smooth at a very high rate of speed...where I rode (not riding right now) speed would be dangerous.
Paso finos... well,,many are not like they used to be. Some are still breeding the more mellow ones. But the onesI have been around..are snorting dragons...great int he show ring,,but on trail...well..lets say they are not relaxing.
There are a few other breeds...Rocky mountiain/Kentucky mountain and so on... that is Chocolate or Silver Dapple with a white mane and tail...ask if their eyes have been checked....many of that color go blind. A friend found out the hard way.
Missouri Fox troters can be nice.
But like any breed you need to figure out what you want..and take your time looking. Even with in a breed some are more talented and smoother than others.
Have fun shopping!