I've dragged them down to the fireplace in the kitchen, just so I don't have to listen to people commenting on them so much. I always take Ulfric's cloths to my house in Windhelm, the second floor of which I convert into a museum dedicated to the war. On one mannequin Ulfric's clothes, on another a Stormcloak uniform, and on the third I always but my Imperial uniform. I also place the sword that used throughout the campaign (Always an imperial sword with a fiery soul trap) there.
When you think about it, a defeated Ulfric really would end up as nothing more than a minor footnote in history, remembered only as a part in the dragonborn's history if at all.