Getting a horse in Chrono Odyssey, you'll soon realize, is a top priority within the first few hours. There are no mobility skills in this game — at least from the three classes we got to try out in the Chrono Odyssey playtest). You do have a sprint button, but it rapidly drains your stamina, and recovery takes a long time. Plus, the sprint is not even that fast.
Chrono Odyssey has a massive overworld that you have to do your homework all over. Naturally, the sooner you get a mount to navigate through it faster, the better.
How to unlock mounts in Chrono Odyssey

Even though the first big town you go to has a stable, you have to venture a few thousand meters southeast to unlock mounts in Chrono Odyssey. Specifically, you have to get to Santove's Discovery bound stone, south of the Shady Vale and due north of Western Vinetrap Forest.
Next, you have to go to Medina, the stablemaster stationed here. She will be easy to identify, because the local quest marker highlights her, and you can pick up the quest Gone With The Wind.
Simply put, Gone With The Wind unlocks the horse in Chrono Odyssey. The quest sends you due east into the grasslands to find Snowy, the white horse. Your task is to identify the all-white horse, walk up to it, and then press E to claim it.
In reality, there are several all-white horses to be found, and claiming either one will do the trick.
There is one significant challenge to this job: the horses will start running away mid-animation when you start calming them. If you have unlocked the Chronotect skill Temporal Isolation, this is quite easy to counter. Simply find the horse and freeze time before you start calming the horse.

If you're like me and didn't unlock this skill by the point you started the quest, it's still possible to do it. The wild horses in Chrono Odyssey have an internal cooldown after they run away from you once, and this also applies to the horse you're trying to tame. In other words, wait for the horse to run away once, and immediately get to it and interact with it.
Once you have tamed it, a "Yes, this is the one!" message will pop up. Run back to Medina to complete the quest, and claim your horse in Chrono Odyssey. Afterwards, talk to her, and select Snowy (the first horse), then select it again till it shows "Equipped".
All the other horses in Chrono Odyssey, at least from what's available in the playtest, are different skins for the same mount. Furthermore, horses cannot sprint, but do have a small double-jump window.
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