To start the quest "Blood on the Ice", you have to had visited and left Windhelm four times. If you have not been to Windhelm a lot, just go there, then fast travel to some other hold (Such as Whiterun), go back to Windhelm, and repeat this process a few times before proceeding.

From the Windhelm main entrance, head north, and then west down some stairs and towards a small graveyard in the street. A corpse lays on one of the tombs, with some people gathering around her. A Windhelm guard will stop you. Ask him what happened. He will tell you another girl was killed, Susanna, from Candlehearth Hall. Ask him if it has happened before. He will tell you it is always the same: Young Girl, killed at night, body torn up. Ask the guard if the murders are being investigated, to learn that they are stretched thin as it is with the war, and noone has the time to spend on this. Ask him if they could use some help. He will tell you to ask some of the gawkers if they saw anything useful.

Open your quest journal:

Blood on the Ice
Windhelm is plagued by a shadowy killer. I've been asked to help investigate the latest murder.

Question the witnesses.

Talk to the three people standing nearby:

Sidla the Unseen: Ask her if she saw what happened here. She tells you she heard a scream and came running, but Susanna was already like this when she got there

Calixto Corrium:  He says he saw a fellow running away, but never got a good look at him.

Helgrid: She did not she the murder, but she did notice that the girl's coinpurse was still intact, so this was not a robbery.

After talking to all three witnesses, report to the guard and tell him you've interviewed the witnesses and none of them had any useful leads. Ask him if you can still help with this. He will tell you to talk to Jorleif to get permission.

Go to the Palace of the Kings and speak to Jorleif. The Palace of the Kings is a big building on the north side of Windhelm. Tell him you heard about the murders. He will tell you he will gladly accept your help, and he will also instruct the guards to assist you in the investigation. He himself will offer you advice from time to time.

Your goal now is to examine the Crime Scene. Head back to where the quest started in. See the pool of blood near the murder scene. Follow the trail of blood to the west (it is recommended you do this during the daytime so that the trail is easier to spot and follow). The trail will lead west up the stairs, then north up through some more stairs and then end on the house to the left, Hjerim. Your objective now is to get access to Hjerim.

The lock there is a master lock, so if you are not good at lockpicking you have to find another way in . If you talk to Jorleif and ask him how to get into Hjerim, he will tell you that it is Friga Shatter-Shield's old place and has been abandoned ever since she was killed. Her mother, Tova, has the key.

If you talk to Helgrid in the Hall of the Dead and ask her if she had noticed anything strange about the body, she will tell you the shape of the curves is strange,  and that it was some kind of Blade used by ancient Nords.

Tova should be around the market (in daytime), to the Southwest of the scene of the crime. Tell her you have some questions about her daughter. When she tells you she'd rather not talk about it, tell her you have authority in this matter and you require her cooperation. Tell Tova you'd like to investigate her daughter's house, but you need the key. She will give you the key to Hjerim. Go back to Hjerim and enter the house. Your goal now will be to look for clues.

First, investigate a blood stained chest on the south wall. From the marks on the floor, it looks like this box was pushed against the wall recently. Search the chest to find "Beware the Butcher! (11)" and  "Butcher Journal#1". Beware the Butcher says: "The killer who haunts the streets of Windhelm! Those calamitous times bring out the worst in people, don't become the next victim! See Viola Giorano if you spot any suspicious behavior". The Butcher Journal#1 appears to be a diary written by the murderer. This will complete the objective "look for clues" and tell you to follow up on the clues from Hjerim, but keep searching the house first.

Investigate the Pots and Pans in the North room. They haven't been used for ages. Nothing but skeever droppings and cobwebs inside. Back south, then investigate the Wardrobe in the western wall. This perfectly good wardrobe was left behind for some reason. Search it to find some fine boots and fine clothes. Investigate the wardrobe near it, to the north. The wardrobe seems to be nailed to the wall for some reason. Open it to find a false back panel. Open the false back panel and go inside to find a horrifying sight of a room filled with body parts. Investigate the altar. The altar is built  to some unknown magic. It looks like someone is using body parts towards some gruesome end. Read and take Butcher Journal #2 from the altar.

Exit the secret passage and inspect the small shelf between the two wardrobes. The shelf is filled with more of those Butcher fliers from around the city. One pile looks misshapen. Pick up all of the flyers to uncover a strange amulet (a valuable one too, valued at 1,000 gold!). Go back to the entrance and climb the stairs in front of it. Examine the Bed and Chairs. The chair is stacked on the bed in an odd fashion.

Exit Hjerim. Talk to any of the Windhelm Guards. Ask the guard if he can tell you anything about the "Butcher". He will ask you if you have been talking to Viola Giordano. She posts those all over the city, and someone keeps taking them down. Ask the guard if he knows what the strange amulet is. He will tell you he has never seen anything like it, and would recommend you take it to Calixto at the house of Curiosities. He has a good eye for strange trinkets. (If instead of asking the guards, you go to Jorleif at the Palace of Kings for advice on the clues, he tells you the same things).

You can follow up on the amulet lead by going to Calixto's House of Curiosities in the eastern part of Windhelm. Ask Calixto Corrium if he knows anything about this amulet. He will tell you that it is the Wheelstone, a heirloom symbol of the power of Windhelm. Traditionally it is carried by the court mage. He will offer to buy it from you for 500 gold. The best option is to sell it to him, as you will be getting the amulet back later anyway.

Next, search the streets of Windhelm for Viola Giordano. Use the local map to find her, there should be a marker indicating the objective position. As you approach her, she tells you to be on the lookout, the Butcher could be around any corner. She is worried about her own safety after what happened to those other women. Talk to Viola. Ask her what she can tell you about the Butcher. She tells you she has been following him for months now, trying to find him. The guards won't help because they are too busy with the war, the people won't help. She is the only one who thinks he can be caught.

Tell her about the Journal you found in the killer's lair which makes it sound like the court mage has been experimenting. She will tell you about Wuunferth. There have been rumors swirling about him for years. But he's a dangerous man. It's why they call him "The Unliving". She recommends not approaching him directly. This information needs to go straight to the steward. He'll listen to you.

IMPORTANT NOTE: To complete this quest faster, you must IGNORE the current objective to speak to Jorleif. Instead, go straight to Wuunferth. Skip the next few paragraphs in the walkthrough, and read again from the next place it says "Important Note". Or, if you want to follow the the objective as listed in the journal (not recommended), read on.

Go to the Palace of the Kings and talk to Jorleif. Tell him you believe the killer is Wuunferth the Unliving. He tells you that it is quite an accusation and asks you if you have proof. Tell him you have evidence of necromancy, and found his amulet. He says he does not want to believe it. Wuunferth has been a trusted friend to Ulfric for many years. It pains him to see that the whispers had truth to them. He tells you that Wuunferth shall be apprehended and thanks you for your diligence in getting to the bottom of this matter. You can follow Jorleif and the guard as they go and arrest Wuunferth. Wuunferth will deny the accusations, claiming that he himself has been scrying over the last few days, trying to find the killer. But Jorleif doesn't believe him and sends him the the Barracks and locks him up in a cell  The streets of Windhelm are now safe. or are they?

Return to Windhelm after 3 days have passed. A guard is standing near the body of Arivanya. Ask him what happened here, if there was another killing. He tells you that yes. He thought the city was safe, that you captured the Butcher. How could this has happened? Tell him the killer must still be out there. He says that obviously, and that you should visit the Bloodworks to talk to Wuunferth. We need to figure out where the evidence went wrong.

This RESTARTS the quest Blood on the Ice:
The Butcher has struck again in Windhelm, after Wuunferth the Unliving was Imprisoned. It appears he may have been innocent. I need to find the real killer.

Objective: Speak to Wuunferth.

Head to the palace of the Kings. Enter the  palace, then take the door to the SE to go into the Windhelm Barracks. Find Wuunferth in the prison cell and talk to him through the bars. Tell him the killer has struck again. Apologize to him and ask him to help you find the real killer. Tell him you found one of his journals, all about necromancy.

(IMPORTANT NOTE: After talking to Viola, you could have gone straight to Wuunferth instead of going to Jorleif. You can find Wuunferth upstairs. After entering the Palace of the Kings, open the door to the left and climb the stairs, reach a room in the end of the Hallway. Talk to Wuunferth. Tell him you've heard he dabbles in Necromancy.)

 He will tell you he is a member of the College of Winterhold, in good standing. They haven't allowed necromancy for hundreds of years. Tell him you found his journals and amulet where the Butcher worked. He will assure you he has never kept a journal and will ask you what exactly the amulet looks like. Tell him it is eight-sided, Jade, ringed with ebony. A worn carving. He will tell you he has heard of it. It once depicted a skull. That is the Necromancer's Amulet, of legend. It appears you were at least half right, there is necromancy at the heart of this. Ask him what you can do now. He will tell you he noted a pattern about the killings. Not that you know that they're tied in to some sort of necromantic ritual, he thinks he knows when the next might occur. From a Loredas of Last Seed until a Middas of Heartfire... It will happen soon, very soon. He tells you to keep watch in the Stone Quarter tomorrow night. That's almost certainly where the killer will strike next. Your objective now is to patrol the streets of the Stone Quarter at night.

Wait until night time, and go to the market in the Stone Quarters. Observe Calixo Corrium attacking and stabbing Niranye or Arivanya. Attack him and chase him if he tries to run away. Catch the murderer and kill him. The go speak to Jorleif for Reward. Tell him Calixto Corrium was the killer. He will thank you and tell you that you have done the city a great service, and that the guards will be more cordial with you in the future. (If you previously implicated Wuunferth in the crime, he will be exonerated and Jorleif will release him).

At this point, depending on how the civil war quests are going, you might be able to buy Hjerim. You must have joined one of the sides to be able to buy the house If you joined Stormcloaks, complete the fourth quest in the series, "Battle for Whiterun", in order to get the option to purchase Hjerim. If you joined the Imperials, then do all the quests in the series to capture Windhelm and assign a new Jarl. Then do the quest for him to find the Helm of Windhelm, after which he will let you purchase the house of Hjerim.

This complete the quest "Blood on the Ice"