There's a 'Joan the Wad' mentioned in the Oxford Dictionary of English
Folklore, who appears in a popular Cornish rhyme as a sort of trickster
figure, a female Jack o'th' Lantern or Will o'th' Wisp, 'wad' perhaps
meaning a torch or lantern.
I imagine that for Shakespeare, the name Joan would have provided a
rural English counterpart to Jack, just as Jill does in the famous
nursery rhyme, and might have been used in some circumstances to imply
a peasant slattern, possibly mischievous and cunning -- but not
terribly bright.
I'm not sure if the trickster element applies to this context though,
where an image of tough hard-working rural folk is being conjured up.
And in that frozen winter, I don't think much cooling of the pot would
have been required!
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