It seems to be possible to trace Let all that are for mirth inclin'd and/or All you that are for mirth inclin'd back to the latter 17th century. Dates of 1684 and 1656 are quoted in various sources, with an assertion that the ballad may actually be somewhat older.

What remains a mystery is the assertion in Wikipedia of 12th century origins, for the Wexford Carol version. I can only imagine this claim relates purely to the Irish text.