Intriguing thought.

My take is that it refers to 'a pot of good ale' in the First Part, the idea being to drink away old grudges with the ale.

Chappell, in his "Popular Music...," says the song is "a pleasant country new ditty; merrily shewing how to drive the cold winter away. To the tune of "When Phoebus did rest" (footnotes), black-letter, printed by H(enry) G(osson)." Too bad that the author is unknown.
By 'countrey', I presume it did not originate in London.
As well as being a song, the 'ditty' recites well. A great one!