The oak tree element is modeled after the Major Oak.

The Major Oak is a large English oak (Quercus robur) near the village of Edwinstowe in the midst of Sherwood Forest, Nottinghamshire, England. According to local folklore, it was Robin Hood’s shelter where he and his merry men slept.
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The logo typeface is Tintern Abbey. A little gothic, a little art nouveau, a little deco, the font could have been popular at the time the Robin Hood story was popularized by the 1938 film The Adventures of Robin Hood starring Errol Flynn.

Tintern Abbey is a place in England and was featured in a notable Wordsworth poem, but has nothing to do with Robin Hood!

In John B. Grimball’s 2005 letter regarding the history of the development, he notes: The 130 or so acres known as Sherwood Forest were, in the early 1900’s, essentially woodlands. The name “Sherwood Forest” was selected by William Gordon Belser, drawn from his love of English literature.