This song is an old round and first appeared in John Hilton’s Catch That Catch Can: A Choice Collection of Catches, Rounds, and Canons, first published in London in 1652.  The name of the song on the contents page is “Come follow, follow me, whether shall I follow” (underline mine). The original words are:

Come follow, follow, follow, follow, follow, follow mee;
whither shall I follow, follow, follow, whither shall I follow, follow thee?
to the Gallow, gallow, gallow, to the gallow, gallow treee.

Wee have oft been Rogues together,
Now we must hang ‘twixt winde and weather:
We have oft time nipt a Bung boy
Neatly, neatly, in a throng boy,
Neatly, neatly, neatly, neatly, neatly, neatly, in a throng boy.

So the song is about a gang of rogues or thieves that one day might get caught and hanged.  At some point the words were changed to the more pastoral ‘greenwood’ words.

Notes by Gwilym Davies , with help from Masato Sakurai, posting in the online forum ‘Mudcat’.  20 March 2016