How to Train Your dragon belongs to Dreamworks and Cressida Cowell
I'm thinking that, no, he does not. Over time, dirt and sweat has gotten up in there and turned into mud, which then hardens into a sort of proto-concrete, thus explaining his gravity defying helmet. And his his lack of head injuries (helmet+mud layer+thick skull). And let's face it, Tuffnut's totally the type to never take his helmet off, even when he sleeps or is forced to take a bath.
It happens more than once, though...
I have to agree that the most plausible theory is the 'wedged on his head' one ;D
Tuffnut: *off-key* I think I'll try defying gravity AND YOU CAN'C PULL MEE DOWN!!!!
Ruffnut: OH YEAH?! (yanks Tuffnut down)