Well I ride Tennessee Walking Horses and the "Chair" seat is the correct seat....as long as you still have your back straight...and your legs are not too far infront of you. Everyone has thier own way of doing things, so each to thier own.
These are just off google.
Western on a TWH
Saddleseat on a TWH
Western on a Non-Gaited horse
Saddleseat on a Non-Gaited horse