Having grown up training Morgans- I couldn't resist. I totally agree that a hard mouthed horses is 'made' by the rider/ driver. They are not born that way- we as handlers make them what they are. So no, harness training will not make them hard mouthed. All our horses are started in harness or at least learn to ground drive before we ever back them. They learn voice commands, the feel of the lines along their sides and around their hocks, etc. Long lining is excellent for tuning up even seasoned horses. Most advanced dressage horses are taught hi level movements with long lining first. Either way- harness or saddle horses should learn how to bend, flex and move off the rider/ drivers aids. Even ranch horses can benefit from dressage work- the better they can bend and give, the faster and more balanced they will be when they turn after a cow. Just an opinion...
I think that there are many horses that can excel in both riding and driving, and then there are some as well that will just take to one or the other more favorably. One of our Morgans that we sold went on to be a versitility champion under saddle in western, jumping, sidesaddle, hunt seat, dressage AND was retired at Walnut Hill Driving Competition (very prestigious carriage show) as a multiple harness champion! I do however think that the more you can do with your horses- the better animal they become. After all- way back they needed a do all horse that took the family to church in the buggy on Sunday and that could also go bring in livestock during the week.
Even our 'prissy'

show horses here get down and dirty. Our halter / show champions are expected to be harness broke, trail rideable, not spooky, and they have all seemed to really take to working the cows at the farm with much enjoyment. Keeps them from getting bored!
So cheers to the Morgan enthusiats- although I love ALL good horses! The above mare is Skyloft Seduction and 5th generation of our breeding program...
www.skyloftmorgans.com