I don't have a lot of experience with halter horses, but in my opinion, I don't see a horse of this build enjoying himself running barrels. Any horses I've seen like this are content just showing at halter and really don't have the motivation to run like you want a barrel horse to.
I'm not going to say it's impossible, I just think if you want to be fair to your horse (at least I personally would) steer clear of events that will put physical wear and tear on him.
Yes I agree with you, I'm am very sure a halter horse could compete in any event you want. Quarter horses (and paints) are great all around horses that are (usually) bred to be intelligent. However, is what you are competing in fair to your horse?
For example, thoroughbreds are bred to be fast. Not thick boned. You don't see a lot of people barrel racing thoroughbreds. Yes, thoroughbreds "can" do anything you ask of them (trail, jumping, dressage, driving, barrels, poles, etc.) but you don't see a lot of people barrel racing thoroughbreds. One of the reasons being, they were not bred with strong bones to stand up to the rigor that it takes to stop 1000 pounds moving at over 30 mph and turn in 360 degrees around that barrel.
I have seen a few very nice barrel horses that were thoroughbreds, but they just don't hold up to that kind of work very long. There is a reason you don't see show jumpers and race horses over the age of 10. They were built to race while they were young, and not much else. Sadly, the same is true with halter horses. They were built to be bulky with nice conformation and not much else. I am by no means putting halter horses down, I'm sure they are very intelligent and capable, unfortunately bred into a massive body.
You could probably try it and see. Your horses isn't going to turn up lame the first time you work through the pattern and if you start slow your horse should let you know if it is experiencing any pain or difficulty at an early stage in training. Possibly when working at the trot or lope.
I would not recommend competing regularly at a rigorous speed. I'm sure it's fine to run the pattern every so often at a fun show though:) Maybe try different events that don't require so much strain on a horse like competitive trail or western pleasure?
Just keep an eye on your horse and have is checked for soundness before hand. Sorry for the huge response:/ By the way, that horse in the picture is beautiful, I don't know if it's yours? I hope I helped some!
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