So I've received a couple messages about this actually. And here are just a few tips on working towards this.
It is a decent grind. I would auto run through the night with my Xbox on for a few extra hours a day.
Horses can auto-run, not auto-sprint
When out of a safe zone, when they move without holding the trigger button, that is considered running. When you hold the trigger, that is sprinting.
So it's a trade-off, you can auto train but you move slower, or you can play yourself and Sprint and run faster.
Then for the paths, I make sure to just try and set straight lines for long distances if possible because they'll slow down if automatically going around corners or bends. My typical path is from Heidel to the West right before the tower pass
You can set the auto looping paths by LT+X and it will loop from your location to where you set. You know it's a loop when the path is green versus one way path that is blue.
If going for the achievement, I suggest leveling lower tier horses because they level faster than higher tier.
As mentioned by PSYCHADELICACE; taming horses does give you a fair amount of XP and can level you faster. There are guides online for loops to run for horse spawns. (There are a couple on the Heidel to the West gate path that I would periodically check). Just need to be aware of the size of your stable, which can be increased through town management to hold more horses.
Horses respawn in each server instance in each location every 2 hours I believe, and can spawn 1-4 horses. It is good to get a path that takes about fifteen minutes to check, and then you can hop to other server instances if doing hardcore horse taming.
Guides online also debate how far to level your horses. I would take them to 15. Some suggest 10, and others even 5 if you plan to tame a lot. I didn't have that much time so I would idle train which took longer. Past 15 is worthless because of the XP needed. When done, you can register the horse on the market for some decent amounts of silver if it has perked out decently enough.
You can also buy a training gear outfit on the Central Market and use the Life XP boosters when the horse is a low level to try and get extra boosts. It is good to invest in these sooner than later, and use the boosts if you do plan to tame horses.
I know you can find additional guides on the internet as the PC version is pretty similar to the Xbox version. But this game is a hefty grind, and there is a lot of information out there over it.
Good luck, and if you have comments or need something clarified, I'll do my best to help but I am by far no professional haha!