Question from +Nobilis Reed.
Answer is: No.
The two are completely different skill sets and it's actually easier to train a horse broken to harness to ride (most dual purpose horses are trained to harness before they are trained to saddle).
Although many (but not all) riding horses are taught to ground drive or long line, that only covers part of their training - and the ground driving used on riding horses is much more basic.
The fact is that a cart is actually a rather large, scary object to a horse. This is why driving horses wear blinkers or blinders, so they don't see the cart (some people argue that this is fine until the tack is damaged...a horse trained to drive with blinders will not drive without them and thus they train young horses without them, although they may use or add them later).
Driving training is an entirely separate thing from riding training. The horse has to learn voice commands not generally used on riding horses, and to respond to only the voice and rein - quite a bit harder for an animal as tactile as a horse.
So don't have your character get off their saddle horse and hook it to a cart unless you mention that the animal is trained for both (which is common today in Morgans, many European pony breeds and cobs/vanners as well as some draft horses).
Ground driving in partial harness (the horse's weird body language is because she's being asked to back up).