Except for protecting ears from cold air, does a woollen cap provide any other significant advantage in winters?
This article is what you need: http://www.bbc.com/future/story/20130708-is-most-heat-lost-from-your-head . Citing an excerpt from it:

[H]aving your head immersed in cold water only adds 10% to your overall heat loss in a cold pool. And given that the head accounts for 7% to 9% of the body’s surface, that doesn’t seem excessive.
But before you throw your collection of woolly hats in the bin, there’s another finding to bear in mind: when the head is allowed to get cold and the body is effectively insulated, the body’s core temperature drops a lot more rapidly than most people would expect. 

In the end, wearing a woollen cap prevents the body's core temperature to drop too low. So if the rest of your body is well covered, you can skip the cap and put just your comfy headphones on; if, on the other hand, your clothes don't protect you well, putting a woollen hat on may be the easiest way to not feel cold.