NUTS IN MAY/ COLD AND FROSTY

Can anybody help with derivation of this expression; used in the childrens song "Here we go gathering nuts in May, nuts in May, nuts in May"
In the northern hemisphere at least, one would expect to gather nuts in May; rather in the autumn or winter!

'Here we go gathering nuts in May
On a cold and frosty morning!'
I remember it from my childhood in Ireland but have not heard it in years. Did you mean one would 'not' expect to gather nuts in May?

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