You get this quest in Whiterun, most likely while you are on the quest to deliver Gerdur's message about the dragon to Jarl. In the market, you overhear a conversation between some Olfrid Battle-Born family and Fralia Gray-Mane. The Battle-Born insist that Fralia's son, Thorald, is dead, but Fralia does not accept this. She believes her son is alive. She thinks the Battle-Born are holding her son prisoner somewhere. But they  keep telling her he is dead, that he died as a rebel stormcloak traitor, Talk to Fralia. She will tell you the Battle-Born are lying. Ask her how she knows her the Battle-Born are lying, or how she knows her son is alive. She will ask you to meet her at her home so she can speak to you in private.

This starts the quest
Missing in Action
Fralia Gray-Mane in Whiterun is convinced that her missing son, Thorald, is still alive and being held captive. She's asked me to visit her at her home to speak privately about the matter.

Objectives: Meet Fralia at her home.

Fralia's home is located to the Nothwest of the market. Set the quest as active and locate it on the local map. Head there during the day or the door might be locked.

When you enter, Fralia is there together with her other son, Avulstein Gray-Mane. Avulstein doesn't trust you, he thinks you are spying for the Battle-Born, but Fralia convinces him to give you a chance. He will ask you if you are here to help. Tell him that absolutely, and ask him what you can do. He tells you he knows for sure that Thorald is not dead. The Imperials are keeping him, he just doesn't know where. The Battle-Borns know something, but they are hiding it. There must be something in that house of theirs. Ask him what sort of proof he needs. He will tell you that he needs anything that proves that Thorald isn't dead, but being held captive.

The quest log will be updated:
Avulstein Gray-Mane believes his brother Thorald has been taken prisoner, and that the Battle-Borns of Whiteburn have proof. I need to find it and bring it to Avulstein

Your objective now is to find evidence of Thorald's fate.

Exit the house, and head Northwest to the House of clan Battle-Born. Use a picklock to break into the house. Try to sneak unseen. If you are spotted by the guard, and have previously been awarded the title of Thane of Whiterun, you can order him to look the other way.

Open the door to the Bedroom in the Northwest. Then unlock another door to the study. On the table, find  the imperial missive. Read it. it says:

"It has come to my attention that inquiries have been made as to the whereabouts of one Thorald Gray-Mane. It is my duty to inform you that Thalmor agents have taken possession of the prisoner and have escorted him to Northwatch keep. I don't think I need to elaborate. It is in everyone's best interest if the matter is dropped entirely. I trust there will be no further inquiries in this matter. Gen. Tullius"

That is the evidence you needed! Thorald Gray-Mane is still alive, and is being held in Northwatch Keep. Steal the book and leave the house. Go back to House Grey-Mane to deliver the proof to Avulstein. Avulstein will want to see this right away. Tell him you have the proof that Thorald lives. Ask him if he is planning to assault Northwatch Keep. Tell him you will join him. He will tell you he will round up as much men as he can in Northwatch keep and to meet him there.

The quest journal now says: Now that I have found proof that his brother still lives, Avulstein Grey-Mane insists on assaulting Northwatch Keep to rescue Thorald. I've agreed to meet him outside the keep to assist in the fight. Your objective is to meet Avulstein at Northwatch Keep.

Locate the keep on the map. You will see that it is quite a distance away, near Solitude, the capital of Skyrim. The fastest way to get there (if you have not been to Solitude already) is to hire the carriage near the Whiterun Stables to take you to Solitude, then from Solitude head west towards the keep. When you get to Steepfall Burrow, turn north and descend to the shoreline. Then keep going west and you will reach Avulstein and his men who are waiting outside the keep.

Talk to Avulstein who will tell you of his plan to kill all the guards and rescue Thorald alive. Your objective is to rescue Thorald from Northwatch keep. Approach the keep from the south, killing the enemies and entering the door near the gate.

Note: There are many guards outside the keep. If you find you cannot defeat them, one strategy is just to make a run to the door. The indoor part of the keep is easier then the outdoors.

Kill the guards inside, then climb down the stairs, and turn right. Head past the tavern, and into a big chamber. Neutralize the archer and climb up the stairs, then turn into a tunnel to the right. When you reach a junction, there will be a corridor with some jail cells to the right, and an interrogation room to the left. Go left and kill the interrogator. Then find Thorald and tell him you are there to rescue him. you need to get him away from Northwatch keep and make sure he stays safe. There is a chest in this room with some good treasure, be sure to loot everything.

Lead Thorald to safety. Go back through the way you came, climb up the stairs and exit the door near the south gate. If there are guards left outside, either kill them if you can, or make a run for it. Once you are in a safe distance from the Keep, talk to Thorald. He will thank you for rescuing him, and tell you he is not returning to Whiterun but instead he is going to join the ranks of the Stormcloaks. He gives you a message to deliver to his mother.

Fast travel back to Whiterun. Find Fralia Gray-Mane and tell her that her son Thorald is safe. She will want to see him. Tell her he didn't feel it was safe to return to Whiterun. She will  be upset that she cannot see him and ask you how can she know that you really rescued him and are not just telling her what  she wants to hear. Give her his message, "Suffer the Winter's Cold Wind for it bears aloft next summer's seeds". Now she will believe that you had rescued Thorald. She will be happy to know that he is alive. As a reward, she gives you a gift, a weapon forged by her husband Eorlund.

This completes the quest "Missing in Action".