Barry,Thanks for pointing out the wassail verse. I had missed that.
Tune HUGRAME2 in DT is a version of "Drumion Dubh" (for 'Hughie Graham" from Scots Musical Museum, #303). The verse you quoted is in "Sommerset Wassail" in DT. Tune there, WASSOMER, doesn't sound the same to me. I think the verse you quoted was probably lifted from "Drumion Dubh", however.
It is possible the Irish song was known in the 17th century. There is a broadside ballad of the 1680's called "Colly my Cow" which has a pseudo-Gaelic chorus, and the song looks like a parody. However, it is in a different meter, and won't fit our tune "Drumion Dubh". A shorter version of "Colly" was sung at Marylebone Gardens in the 18th century and Baring-Gould collected a traditional version, published in 'Songs of the West'. His tune is unrelated to the Irish one. In spite of the fact that there is no solid connection, in O'Neill's 'Music of Ireland' we find an alternative title for "Drumion Dubh" given as "Colly my Cow".