Go to Riften and enter the Bee and Barb Inn . In here, speak to Louis Letrush . Leave the Inn and go to the jails (they are easy to find with the map marker). Speak to the guard and tell him you’re already allowed to be down here (this MAY be a speech requirement, I am unsure).
Go on through and speak to Sibbi. Talk to him about his predicament and when you get the chance, persuade him and you’ll receive a key to his lodge (you can also get a key to a chest by threatening to tell Maven). Time to go there. There are two mercenaries outside, so take care of them and head inside. Go down the stairs to the right and grab Frost’s papers and the stash of Gold from next to the stairs.
This lodge has 4-5 mercenaries in it as well, by the way, so you could go on a killing rampage if you wished. Why would you want to do that? Well, the house has treasure chests all about and taking out the guards makes looting that much easier. The big catches in this place are the SNEAK skillbook named "Legend of Krately House" and a rare 'Stone of Barenziah', both located in an upstairs bedroom.
Now leave the lodge and follow the marker to Louis Letrush. Give him the horse and you’ll end the quest. Alternately, you can choose to either persuade or threaten Louis to KEEP Frost for yourself. This of course nets you a horse without spending any money at all, and is quite a reward.
HOWEVER, you man want to think first before doing this. For example, what if you have another horse, such as Shadowmere? I tried taking Frost while having Shadowmere and just like Shadowmere, Frost will follow you wherever you go, but Shadowmere is (from a fighting/endurance standpoint) MUCH better than Frost.
When I took Frost while having Shadowmere, I could no longer find Shadowmere. If you have NO horse, then by all means take Frost. Just be careful about taking him if you already have a horse. Either way, once you’ve dealt with Louis this quest will be over. A rather short one this time.