I have used my TWH for the local level gymkhanas -- mind you I am not competing for anything, just out having a bit of fun. My barrel time is roughly 34 seconds (don't laugh) and my pole time is a bit higher. I have also done the flag race with him as well. I also use him for my riding lessons and we are doing a bit of ground pole work and we will try jumping a bit later. Am thinking I would like to complete an endurance or competitive trail ride next year as well. Oh and apparently, he was broke to drive as well but I haven't tested that theory out yet because I don't have a cart and harness. I have also heard of TWH's that jump as well.
Don't know if that statement has much truth to it, but I do know that my dear little TWH can "haul a$$" when he wants to. I mean, he's still not as fast as the quarter horse I ride with, but he really doesn't "know" that he is allowed to go fast yet

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I am thinking that because they use their hind end doing their running walk, that they may have a lot of untapped power

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You know -- if your horse has the talent for the sport or discipline you want to do, breed doesn't really matter.