Roxburghe Ballads (ed. William Chappell, I, 84-88) prints 12 verses as issued by Henry Gosson during the second quarter of the 17th century. Chappell descibes this a reprint of a 16th century piece. He also gives the text, with tune, in Popular Music of the Olden Time (1855, I, 193-195), with more on its history; it becomes clear there than his dating of the song to the C16 rests on a "sacred parody" appearing in A Compendious Book of Godly and Spiritual Songs (1567) which has the same rhythm and a similar occasional refrain.

Thomas D'Urfey (Pills to Purge Melancholy, 1719-1720, IV, 241-242) prints tune and 5 verses (as A New Song. The Good Fellow), variant in some details from those quoted earlier. The tune Drive the Cold Winter Away (which appeared in Playford, Dancing Master, 1651-c.1728) derives its title from the song, for which Gosson's broadside prescribes When Phoebus did rest, which is apparently an earlier form. Simpson (British Broadside Ballad and Its Music, 1966, 197-199) goes into further detail, quoting music from Starter's Friesche Lust-Hof, 1621, and from Playford. See the late Bruce Olson's earlier post in this thread for references to those two tunes, in abc format on his website (currently only available online via the Internet Archive).

Both DT files (see links above) are effectively identical, though for some reason they have been given different titles. They may have been copied from The Oxford Book of Carols (which uses 4 verses of the D'Urfey text, a little edited) or perhaps from the McKennitt record (I think OBC was her source). There isn't much to choose between them: the first is laid out in 4-line stanzas (should be 8 lines each), while the second contains uncorrected typos.

The Oxford comment "the first two verses are by Tom Durfey" is wrong, incidentally (they were in print before he was born); though he may well have altered them a bit.