You can't really create super horses anymore, since the max amount of DS that can be used is 5. Old super horses were made immortal and given a special DNA boost.

To jump, you go to your horse's page OR the jumpoff page, and click "Add to jumpoffs". Then the game automatically jumps your horses every day (for now, but manual jumping is on its way back). Horses with no items will jump each other, and horses with items will jump each other. If you go to training, you will see all the breeds listed. You use horse jumps to raise training boosts for whatever breed you're working with, 5 jumps get you the maximum boost.

Strength is now dependent on jumping, and your mares' strengths will go to 0 if you breed. Pregnant mares are taken out of jumpoffs and you'll need to add them again after they give birth.