Their complaints have nothing to do with trash. Windhelm would have supplies if Ulfric could learn basic management like sending two or three good men to work the lumber mill in his Hold.
Where is Windhelm's steward for all of this? Daily duties of the Hold are the job of the Court Steward, if Ulfric is so busy with fighting the war, why can't the steward handle it? Perhaps if Ulfric spent less time being self absorbed in his own image, he could assign his steward to handle the minor complaints.
Edit: Ulfric is facing a major problem, he has civil unrest in an entire district. Unchecked that could turn into revolt overtime, with the Argonians working the docks unhappy too it could easily mean weapons and gear smuggled into the city. They already rally behind Free-Winter, there is only so much pl*** you can take before you fight back. Did the Nords learn nothing from the native uprising in the Reach?
Maybe that Imperial 'shrine' is just the first step, it could mean they're able to smuggle things into the city.
So now, "children of Skyrim," you have the truth of it. You may call this province home, but you can no sooner claim to own it than a cow can claim to own its master's field. You are just another breed of domestic animal, grazing stupidly while higher beings plot your slaughter.
http://www.uesp.net/wiki/Lore:Dunmer_of_Skyrim
Yeah, I'd say you're screwed. Shouldn't have ignored them. Stormcloak Skyrim is looking at some interesting issues with the Forsworn when you try to enslave them and a could be Dunmer rebellion in the future.