Princess Zelda's runaway Golden Horse is a must have addition to your own stable of mounts, and while it's a bit of a slog to capture, it's worth it.
Zelda: Tears of the Kingdom is Breath of the Wild but better, is the general consensus. Nintendo has built on a lot of the existing elements and rolled out a ton of new ones; but one of the things that hasn't changed is horses. You can even import your Breath of the Wild horses to Tears of the Kingdom if you feel particularly attached to any of them.
And just like Breath of the Wild's Royal White Stallion, the Tears of the Kingdom Golden Horse is another royal mount that offers excellent speed, and strength, as well as a fancy new saddle and bridle to boot. You may have even caught a glimpse of it at Snowfield Stable already before you start the related quest and it bolts. It's not made for hauling carts around but if you want to traverse Hyrule in style, with a horse that has max strength and speed, the Golden Horse is it.