The mystery has been solved!
If you're a fan of Riverdale (tbh don't know why we bothered asking because ofcourse you are) then no doubt at somepoint you've wondered why Jughead Jones aka Cole Sprouse always wears that crown-hat thing??
Well Cole spoke about the hat and it's actually got a pretty cool back story:
It's called a 'whoopee cap' and was a popular accessory back in the 1940's when Jughead made his comic book debut.
"[I] did a lot of research on the cap when I first got the part." he said. "Here's a great little video that does a better job than I could explaining it."
So trusting Cole...Here's the video he was talking about: