Etymology
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wooly (adj.)

also woolly, 1570s, "resembling or made of wool," from wool + -y (2). Meaning "barbarous, rude" is recorded 1891, from wild and wooly (1884) applied to the U.S. western frontier, perhaps in reference to range steers or to unkempt cowboys. Related: Wooliness.

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Definitions of wooly

wooly (adj.)
having a fluffy character or appearance;
Synonyms: flocculent / woolly
wooly (adj.)
confused and vague; used especially of thinking;
Synonyms: addled / befuddled / muddled / muzzy / woolly / woolly-headed / wooly-minded
wooly (adj.)
covered with dense often matted or curly hairs;
Synonyms: woolly / wooly-haired / woolly-haired
From wordnet.princeton.edu