My last year of 4-h, I qualified to go to state in both dressage and pole bending on my old TB, we won our dressage class and were 4th in the poles. This horse was an ex-eventer, Accomplished Equitation horse, had competed to Prix St. Georges dressage, team penned, and was a fun horse on the trail.
My personal take on this is, a horse can do lots of different things, but some disaplines are best done "by themselves" due to the nature of the disapline and how it many contridict other disaplines.
I think trail riding is something that can and SHOULD be done by all types of horses. I know many hunters who practice basic dressage with their horses to maintain responsivness and suppliness.
As for barrels and cutting...Depending on the horse, barrels can ruin a horse's mindset. I owned one it did not, but I've seen it happen. Many a good horse has been mentaly incapable of doing anything else but barrels.
As for thr rider, I have been told my many folks they prefer to see people start out english to establish a better seat *shrugs* I dont know if its true or not, but I knw Im thankful for my drill sergents...er, instructors when I evented and rode dressage making me do painful exercises to make sure my seat was there.
When I am asked what was the hardest thing switching disaplines(when I went from dressage to western, first barrels and now reining) It was the lack on contact. English horses are ridden on more contact then a western horse and this was a huge hurdle for me to overcome.