I heard this tune on the radio this morning, used in a carol by
English composer John Rutter. I don't know who was first, Rutter (born in 1945) or the Frosty Morn ad agency's composer. Or, maybe it comes from an old folk melody. But it is uncanny, the similarity with the tune of the verse ("The height of a piggie's ambition.....")

And of course, Rutter lived in England, so may never have heard the Frosty Morn jingle

http://www.amazon.com/gp/recsradio/radio/B0000031HZ/ref=pd_krex_dp_001_019?ie=UTF8&track=019&disc=001

Sample of Rutter carol