In 7.2, every class will get a class mount. They will all be flight-capable so that you can take to the skies once Broken Isles Pathfinder Part Two is completed (which might take a while, as you need exalted reputation with the new Legionfall faction.)
We got a little preview at Blizzcon, but for those Frost or Blood Death Knights who weren't all that keen on riding around on a fel-green drake or similar, here's some good news: the class mounts are coming in different colors. In effect, there are multiple mounts for each class that are all color variants on the mount.
At this time I don't know how one acquires the alternate colors of the mounts - it's possible you make a choice when you complete the quest at the end of the campaign chain, but I'd hope you can acquire all of the mounts for your class (for example, using the elementally-appropriate Mage disc for your current spec.) I'd imagine you might just have to pay gold for the other colors, but it remains to be seen.
MMO Champion has a page with the current models. As you can see, some classes have as many as four color variations while a couple, like Monks and Shamans, currently only have one. That being said, I'm almost totally certain that this is just a temporary PTR thing, and that they might still be deciding on the palettes of the alternate mounts for various classes.