Promises to Keep

Walkthrough
While at The Bee and Barb in Riften, the Dragonborn is approached by Louis Letrush.

Listen to Louis Letrush's offer
The Dragonborn can then listen to Louis' offer which is to steal a horse promised to him by Sibbi Black-Briar before the latter was thrown in jail.

Speak to Sibbi Black-Briar
If the Dragonborn accepts the offer, proceed to the Riften Jail to speak with Sibbi and get more information. During this conversation, Sibbi will explain that the horse is at Black-Briar Lodge, along with his papers. Additionally, Sibbi can be convinced to give up the key to his stash at the lodge as added incentive.

The Dragonborn can choose to tell Maven Black-Briar about this little escapade or not. If the Dragonborn does tell Maven, the latter says to go ahead with the plan and nothing is ever mentioned about it again.

The Dragonborn must then proceed to Black-Briar Lodge which is guarded by a number of mercenaries. Dispatching the ones outside will yield a key to the lodge (there are multiple copies). Once inside, he or she must make their way down to the cellar to obtain Frost's papers.

Note: Instead of taking the front door it is possible to sneak in by the side door.

Note²: There is also an Unusual Gem in the upstairs master bedroom which can be taken at this time.

Steal the Lodge Stash
If the Dragonborn obtained the key, open the strongbox with Sibbi's stash and take it.

Steal Frost's Lineage Papers
In the same area of the cellar, the Dragonborn will find Frost's papers.

Steal Frost
After leaving the lodge, Frost will typically be somewhere out front, though not usually in the stables.

Return to Louis Letrush
The Dragonborn can then ride Frost to meet up with Letrush, and hand over the horse and the papers.

Where does Letrush actually ride to?
If the Dragonborn not only hands over Frost but then chooses to follow Letrush as he rides away, it becomes pretty clear that Letrush and Frost have little chance of surviving their escapade. So the Dragonborn will have many enemies to fend off on their trip: vampires, bears, sabre cats, bandits, frostbite spiders, wolves, and even a troll. On their odyssey the two pass through Fort Greenwall, to Shor's Stone, past the Windhelm Stables, to Mixwater Mill, the Valtheim Towers, to finally end up at the Whiterun Stables. There Letrush simply disappears from the game, leaving behind Frost. Frost cannot be interacted with though.

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