I have a feeling that it must be Scandinavian; at least I'd never heard it before I came to Norway and here it's something that every pre-school child knows as part of their basic repertoire. Unfortunately only one verse in Norwegian as well so far as I know (but you could always do it in English, then in Norwegian...:-) Here's the Norwegian version (it's almost the same in Swedish and Danish, and is equally well known in both countries):

Min hatt den har tre kanter
Tre kanter har min hatt
Og har den ei tre kanter
Så er den ei min hatt

-mike-