I remember "Puff the magic dragon" from the 1960's, probably Nina and Frederick (an attractive and sympathetic Danish duo) but didn't take it into my repertoire until turning solo in 1992. I am aware of its Vietnam associations as perceived by the USA in general but for me it was always a very tender, slightly sad (having to grow up Peter Pan-like) song for children. If it were not for the Vietnam connection then indeed I would classify this song as a children's song.
The version I sing was obtained from one of Wilfried Drygala's songbooks.