Talk to Rensa at the Dueling Peaks Stable. He wants to see if you can tame a horse and bring it back to the stable in less than two minutes.
The spotted horses out by the Dueling Peaks Stable are much easier to tame since they require less stamina. Once you have got a horse under control, bring it back to Rensa. There is no need to register the horse, so if you already have five favorites don't worry.
Rensa will give you a purple Rupee worth 50 Rupees as your reward.