There are Olympic level horses that are draft crosses! The Friesian is a draft but does a great job of dressage.
Warmbloods are just a mixture of Hot & cold blood horses - Hot being the TB & Arab and cold being the draft horses.
True a horse built and moving to do a particular job will be more succesful as in all disciplines.
My Clydesdale can piaffe in the paddock when the mood takes her - she needs to get pretty excited though! Her extended trot is lovely and we are working on this at the moment on the lunge.
She tracks up beautifully in working paces and carries herself nicely. At some time I will try to get a movie of her working. We start dressage competitions this coming winter. She also jumps - out of her paddock.
I'm currently trying to decide what we plan to do in the future show wise. Clipped right out she is a lovely heavyweight hunter type. With feather she is a prime example of a Clydesdale. Sadly I can't do both successfully - feather on for one discipline and off for the other.