'Greensleeves' is surely only perceived as a folksong by the general public. I can't think of anyone who knows a little about the subject who would think of it as a folk song. Vaughan Williams set it as a folksong in a classical setting which I suppose might have had some bearing on people regarding it as a folksong. Whilst it's one of my favourite tunes I would never regard it as anything but artsong. The tune in a much corrupted state has been used in various folk contexts and I've actually sung a 16th century ballad set to it. I can't imagine it actually having been a folksong in the 16th century. It was very much a court song even if Harry didn't compose it and the ballad I sang it to was about a whole load of nobility at an archery contest written by one of the century's most celebrated balladists.