Nobody mentioned that the Plantation Saddle, as pictured below, (Steele version) Steele Plantation Trail Saddle
to ride the TWH. It is technically, a type of SaddleSeat saddle, with English irons, and no knee rolls, usually cut back at the pommel to accommodate a horse with prominant withers.
In the agricultural pre-CW South the population was much lower than the north, with few towns and good distances in between them. It was natural that gaited horses would be preferred to get you comfortably around, and yes, they rode "English." We own a very old plantation saddle--sorry, don't know where the pictures are of it, but I'll take some this weekend--and it's almost identical to the site above, just without the fancy tooling.