I have a Doc Bar horse too! There is a very very reputable trainer here in Nebraska that seems to know a lot about certain bloodlines and he told me some things about the Doc Line that really hold true about my horse. Doc horses are intelligent, and sometimes too smart for their own good. They also are mostly go with little stop. Meaning all they want to do is go go go go, faster faster faster. That is very true about my horse, he isn't satisfied until I have let him have a good run. They like complicated work and get bored easily and tend to act up when bored....also my horse to a T.
I think Cinny is one of the few Doc horses actually being used for Dressage. Usually they do more cowy things like Reining, Cutting, barrels, etc.