From Smithsonian dot com:
Nothing says “princess” like a pointy, cone-shaped hat. From kids’ costumes to medieval paintings, the cone hat—more formally known as a hennin (or henin)—is a sure sign of royalty. But here’s something you might not know about the hat that adorn the heads of pale-skinned ladies: they were actually modeled after the hats of Mongol warrior queens.Medieval PoC points to the book Secret History of the Mongol Queens, where author Jack Weatherford writes:The contraption struck many foreign visitors as odd, but the Mongol Empire had enjoyed such prestige that medieval women of Europe imitated it with the hennin, a large cone-shaped headdress that sat towards the back of the head rather than rising straight up from it as among the Mongols. With no good source of peacock feathers, European noblewomen generally substituted gauzy streamers flowing in the wind at the top.