The Royal White Stallion

"The Royal White Stallion" is a Side Quest in.

Overview
Link obtains the Quest by speaking to Toffa at the Outskirt Stable. There, Toffa tells Link of a BotW: that his grandfather claims Princess Zelda once rode. Toffa also explains that a traveler recently mentioned seeing a Pure-White Horse atop Safula Hill, prompting him to ask any willing travelers to return to the Stable with it so that he may see it for himself. If Link accepts his request, the Side Quest will begin.

If Link tames the White Horse before accepting the Quest from Toffa and brings it back to the Stable, Toffa will implore that Link register the Horse at the reception desk right away, and to come speak to him after.

After registering the White Horse with the Stable, Toffa will grow excited over the fact that his grandfather's stories were true and give Link the Royal Saddle and Royal Bridle as thanks, completing the Quest.