Medieval fools: to hat or not to hat?

On his blog Got Medieval, graduate student in Medieval Studies Carl S. Pyrdum, III spent his most recent April 1 contemplating the depiction of medieval fools and their headcoverings - or lack of them.

The article includes period artwork of fools.

Pyrdum writes:

One thing you might not realize about fools is that the pointy-hatted, bell-jingling fool like the one in the image at the top of the post is more a Renaissance thing, or perhaps more properly a Renaissance depiction of what Renaissance artists thought a proper medieval fool ought to look like. (Really, to tell you the truth, most of the pieces of medievalia you associate most with the period are actually parodies from the Renaissance or Victorian re-imaginings, but that’s a tale for another time.)