Quick Q. Training and riding school facts?

What happens if you train your horse in the wrong discipline during daily training?

Also what about the wrong discipline during riding school?

It seems that stats gained are still for the right discipline but what about training exp?

If you train your horse in the wrong discipline, it will still get a training point, but you will not gain player experience. (Or you will receive less experience, if it's the wrong discipline but the correct grade.) You receive the most experience when you train a horse in an arena of the correct discipline and the correct grade.

There's a slight monetary bonus for riding your horse in a school with the right discipline, but it doesn't affect the stats they receive.