You had done BoTI before? Cause I didn't think you could even buy the house til that quest was done. If you had, I'd say the game was a little confused.
The house is suposed to be empty during that quest and I would think had it allowed you to furnish the house ( and clean it ) it would cause a problem with the quest. Which maybe why you couldn't furnish it... stretching as I don't know if you did the quest or not.
I finished the CW quests on the Imperial side and never touched Blood on the Ice until it was all over. I had to buy the house just to get BotI to start because when I walked through the cemetery there were no guards and no murder victim, just the three civilian NPCs standing around where the victim would otherwise be found. Couldn't initiate by talking to them or any other random guards either. Since I had the money anyway and had already been granted the right to buy property, I just went to the steward and bought the house. He did not offer me any options to furnish it (which I wouldn't have taken anyway just in case). Once I entered the house the quest started, I did the required investigations in the house and finished it off from there... although I was smart enough this time to go talk to Wuunferth before taking my suspicions to the steward, lol, which meant I didn't have to leave town long enough for another murder to occur.
So, yeah, you can buy the house before you even start BotI and if you haven't started it yet it will start the first time you go in the door. I think they did fix something so that if you buy it under those circumstances you don't get the options to buy furnishings until doing so won't cause any problems with the quest.