It is rash to speak of "the" tune to this song -- or of "Froggy Went a-Courting" for that matter. I don't happen to have heard a tune that fits both, but that is no surprise. Of the two for The Wheel that I have heard, the Vermont one was rather nondescript (scale DRMFSLTdrmfslt; dots mean continuation for a beat):
Sd.ddrmr.TS.
Sr.rrmfm.rd.
mf.fL.fm.mS.
mr.rrmfm.rd.
The Scottish one was Old Hundred!