Get a Unicorn Horn
Do your best on all of the Free Ride competitions, then go to the quadrangle and get a time of 24.09. You should be told that you beat the top score. At the very top, a sign should appear, stating that you won the Unicorn Horn. Go to the stable and go to costume horse. At the bottom, it should read "Horn". It may take some turns until it will say that. Keep trying until it happens.
Get more hearts
After winning the first buckle, go to the competitions then go to "Unrank". Win five times and you should have five hearts, which is the maximum.