Sh'mot 34:29 tells us that when Moshe came down from Har Sinai with the second set of tablets he did not know that קָרַן עוֹר פָּנָיו בְּדַבְּרוֹ אִתּוֹ -- horns of light were on his face from his speaking (with God). The gentile sculptor Michelangelo depicts them as short, knobby horns, similar to those that young goats have, if this city-dweller understands correctly. But that's not very stately, not the sort of thing you would expect as a divine symbol, and anyway we shouldn't trust the source to be familiar with our mesorah. Oh c'mon, the same guy painted God as a man, as if such a thing were possible! So surely this work has no hechsher (unless it's this one).
So the horns probably didn't look like this:
But what did they look like? Perhaps they looked like ram's horns, to remind us of the call of the shofar at Sinai even after the people moved on from there:
But that seems impractical if we assume that he needed to be able to lie down and sleep each night for the next forty years. So maybe the horns were more like this:
But if so I can't determine what meaning we should take from it, nor have I found any source that might support it.
So maybe all of these are wrong. And anyway, it says on his face (panav), not on his head (rosho), and none of this reflects that.
What did Moshe's horns look like, and how do we know?