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Speak with Snak gra-Bura at the Chestnut stable near the Imperial City. If you have a horse tagging along, you can put some armor on it. It's just 500 gold, may as well.
It is recommended doing this with a black horse as it is the fastest horse (up for sale) in the game. The only horse stronger is the white horse. So you can have the fastest horse with the armor to make it a lot tougher. These things combined makes it a pretty good horse. The only thing better would be to do the Dark Brotherhood quest to get Shadowmere.