The Highmountain Thunderhoof mount is obtained by completing the Highmountain Tribe recruitment scenario. Once you complete this quest you will get the mount, which is usable on any Horde-character. The recruitment scenario itself begins in Orgrimmar, and is both fast and easy to complete, but you need to fulfill the following three requirements first:
1) Have Battle for Azeroth purchased on your account.
2) Complete the story achievement in Highmountain called Ain't No Mountain High Enough. Basically you need to do all story quests in Highmountain, and most people will get this while leveling up.
3) Be exalted with Highmountain Tribe. Do lots and lots of World Quest, and don't ever skip out on a Highmountain Emissary quest, and you will get this pretty fast.
Once you have done this, head to Orgrimmar to do the quests and get your Highmountain Thunderhoof mount.