Activating the quest
While you're in Riften, visit The Bee and Barb inn. In the corner of the main room you will see a balding man - Louis Letrush. Speak to him to learn that he was tricked by Sibbi Black-Briar, who was supposed to sell him a horse. Eventually however he was thrown in jail and doesn't acknowledge the agreement anymore. He did however receive initial payment, therefore the whole case isn't finished. You should head to the jail, speak to Sibbi and explain the case.
New main objective: Speak to Sibbi Black-Briar
Head out of The Bee and Barb and go to Riften Jail. Head inside and you will be stopped by a Guard. In order to get pass him, you will need to either bribe or persuade him. Having solved the problem, go to the cell where Sibbi is. A short conversation will let you realize that you're dealing with quite a cheater - the man doesn't even own the horse that he wanted to sell to Letrush. Formally, the horse belong to his mother, Maven Black-Briar, who most of the town fears. You however don't have to worry - as long as you don't tell her about the case, she won't connect you with it. What's interesting, if you do tell her about the whole case, she will tell you to follow her son's plan. Revenge is a dish best served cold and Maven will take hers after you finish the quest.
The prisoner obviously cannot bring the horse to the buyer - but you can. You will have to steal the horse's (Frost) lineage papers and then the animal itself. If you threat Sibbi that you will tell his mother about everything, he will also give you Sibbi's Stash Key, which you can use at the Black-Briar Lodge. The horse is also there.
New main objective: Steal Frost's Lineage Papers
New optional objective: Steal the Lodge Stash
Head to the Black-Briar Lodge - it can be found east of Riften, right beside the mountains. When you arrive there, it will turn out that the building is well guarded - if you come too close, the Mercenaries beside the main entrance are sure to attack you. Therefore it's best to approach the building from the west - no one guards the door there and the lock can be easily picked (in can be seen in the screenshot below, on the left). Of course you can also steal the Key to Black-Briar Lodge from one of the Mercenaries - it will make the whole mission much easier. The building can be also accessed through a different entrance, though keep in mind that it will be difficult
The documents you're looking for can be found at the basement of the house - enter through the door to be closest to the destination point. Steal the documents from the desk and afterwards turn left - there you will find a stash, the key to which you got from Sibbi (if you don't have it, you can always play with lockpicks). Afterwards head out of the building.
New main objective: Steal Frost
Stealing the horse cannot be done quietly. Sneaking by doesn't make sense - the enemies will notice you as soon as you get on the horse. Therefore it's best to just quickly run to the stable and jump onto the mount. Now you will have to flee the house - remember that by pressing ALT you can make the horse run faster, which will definitely come in handy.
New main objective: Return to Louis Letrush
After stealing the horse and running away from the scene, you are left with two options. The first implies going to Maven Black-Briar and telling her of everything. It's not the best solution, as you will not only not receive any prize, but also come across the massacred body of Letrush sooner or later. Therefore it's best to return to the man and give him the horse.
This solution has a couple options as well. If you just hand him over the horse, you will receive a payment in gold. If you use persuasion and threaten that you will tell Maven of everything, the horse will be yours but you can expect that Bandits sent by Letrush will attack you. Threatening him with death will have the same result. If you don't want to fight the thugs, you will have to satisfy yourself with cash - that way you will end the whole thing once and for all.