The Saltwater Seahourse is an underwater mount added in World of Warcraft patch 8.1, and it's part of the Island Expedition system. In contrast to most of the Island Expedition mounts, it's not part of a random loot system, but you can instead work towards getting this by doing a lot of Island Expeditions.
In order to get the Saltwater Seahorse, you need to buy it from Captain Klarisa for Alliance, or Captain Zen'taga for Horde for 500 Seafarer's Dubloons. These two NPCs are found just next to the map where you que up for Island Expeditions, and they also sell a lot of other cool stuff.
Anyway, the only way to get Seafarer's Dubloons is to do Island Expeditions. Most wins will give you a bag of them, which can contain a lot of Dubloons, even though it most normal to get between 4 and 7. It is also possible to find a bag of Dubloons randomly on the island as well, so keep your eye on the ground to find these lootable objects.
You will need to get all the 500 Seafarer's Dubloons in a single character since these are non-tradeable. So you will need to do a lot of Island Expeditions on your favorite character if you want to get this underwater mount.