According to the guide you have to enter and exit Windhelm 4 times.I don't know it that means the city itself or the whole cell.
I worked on this quest with my buddy for two freaking hours and we followed it online to exact specifications.
We teleported out of the city to another, then re-entered windhelm from the stables each time during the evening. We did it 5 times I believe before entering the final time. There were people at a grave stone which were examining a body and once you speak with the guard there it initiates Blood on the ice.
I don't believe this quest is even able to be completed past a certain point in the game as I was a bit farther into it then my friend was and had to force it all through console and then spend 3 hours cleaning up evidence and cobwebs >.>. Even after completing the quest perfectly each step, we still had to force the steward to offer the house with the 'say' command.
If anyone is lucky enough to complete it like he did (even though he still had to use the say command at the end), remember to clean house option first with the steward and then leave and check your house to make sure. Then buy all the decorations and it should be a pristine house. If you don't pick clean up first the option will disappear entirely from the stewards list and you will be stuck with it or have to delete everything manually to make it clean.
So long story short, it can be buggy either way you do it whether its forced through console or done properly through quest there can still be a screw up somewhere, since it was meant to be a more complex storyline involving multiple npc's and span over several days, as well as have a couple different outcomes with the same reward in the end. The quest was fun to us while we were not struggling with it, and I hope they fix it ASAP, the house is great to have.