When starting either the first or second race, let Ingo get out in front of you. Then, start racing along the outside of the track without speeding up Epona. Eventually Ingo will stop whipping his horse, because he disappears. Then, just ride to the finish line. If you do it on the second race, just repeat the process and you will get Epona. You may need to cross the finish line twice on the second race. Note: This may not always work.