It really depends on the individual horse..I've seen TBs run barrels before, some are good at it and some aren't. IMO, a TB can run barrels but they just aren't built for it like a QH is. TBs are more of a delicate build and are fine boned..By no means am I knocking a TB, they are my next favorite breed..TBs are built for speed and sprinting, the hard stopping, rating, and turning is really what makes a barrel horse, not the speed, even though that's a key factor and the sport is about speed..If all you have is speed and no rate or sitting ability you won't have great success..Like I said before, some TBs can be good at it, but most just aren't built for it and can't handle the stress on their bodies..It all boils down to each individual horse..Heck, even some QHs aren't built for barrel racing and can't handle the sport...Just because you have a certain breed doesn't mean it's going to be good at what it was bred to do..
I actually have an QH/TB appendix mare who is my most consistent horse and my "go-to" girl..She's got the small build of a TB but the legs, head, and butt of a QH..awesome mix.