The Oxford Dictionary of Nursery Rhymes (1951) calls this a "folk-chant"... which is "likely to be exceptionally old". Later it says, "The hunting of wren on Christmas morning (latterly on St. Stephen's Day) has been described by many folklore writers from the time of Aubrey (1696)..."

It seems to come from The Isle of Man and it was originally in the Manx language.

We'll Go to the Wood, Says Richard to Robin - English Children's Songs - England - Mama Lisa's World: Children's Songs and Rhymes from Around the World  - Intro Image
We'll Go to the Wood, Says Richard to Robin - English Children's Songs - England - Mama Lisa's World: Children's Songs and Rhymes from Around the World  - Comment After Song Image

Thanks and Acknowledgements

This rhyme and the 2nd illustration can be found in The Only True Mother Goose Melodies (published and copyrighted in Boston in 1833 by Munroe & Francis).and The 1st illustration can be found in The Sleeping Beauty Picture Book, illustrated by Walter Crane.

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