There is nothing wrong with carefree rides or just relaxed rides. Not only do people enjoy it, but the horses enjoy it also! Riding position is nothing more than making yourself look "pretty" on a horse, and really does nothing for balance or how the horse moves (unless maybe you are trying to do the high level moves like piaffes, etc). When riding bareback for example, you aren't going to have "pretty equitation" then, and it's more important to first off, stay on, and not hurt the horse's back in any way by bouncing while trotting.
HorsesAreForever, Chance is a beautiful little mare, and I think she'd excel in any discipline that you chose for her.
you may not realize it but when you get on your horses back and don't try to stay balanced and in the right place you are actually making your horse look and move worse then on his own. :)
Excuse this if you find this rude, but who in their right mind would get on a horse and NOT try to stay balanced. Even a kid who is learning to ride tries to stay balanced. The rider looks perfectly balanced to me...and no being in the "right place" has nothing to do with how the horse moves or looks (unless you are on their loin or way too far forward).
Silly dressage people ;) and my friends always wonder why I ride western (forgive me if that's rude, I just find that alot of dressage riders, not all mind you) are too concerned about their "equitation" and how they look in the saddle than alot of other stuff.