The woman I work for now has a 15.2 hand solid bay app that she is doing barrels with. He is in the finishing stages and has not competed yet but boy oh boy does he have some promise! He is fast, but even better he is quick, he is super with her turns which she likes better than overall speed.
Remember: Speed is good, but consistancy and form are even better.
Edit: I'm no barrel person, that is just what my freinds have told me... I like slow and steady