I honestly believe most educated adults know what a cocktail hat is, even if they can't articulate it. They instinctively know what one is when they see one. I think I've known what one is ever since I picked up Mademoiselle and Glamour magazines and read them on the sly in the library as a teenager. In the spirit of fairness, I could see how some adults wouldn't know what a cocktail hat is. They aren't worn often anymore.
For those not familiar with this type of a topper, I searched online for a dictionary definition of a cocktail hat. The closest I came to finding one is this. If I get more time I will check Valerie Steele's Enclopedia of Clothing and Fashion at the library. Cocktail, as an adjective, means it's suitable for wear on semiformal occasions. That doesn't tell me very much. I mean you could wear a cowboy hat to an evening soiree. Does that make a cowboy hat a cocktail hat? No way! I like what Carolyn Busch, owner of Fino Fino, has to say about cocktail hats. She says the cocktail hat was called such because it was usually worn in the evening. It is simultaneously seductive, romantic, and feminine, as Busch says.
How would you define a cocktail hat? Tell me about the very first cocktail hat you can remember.