woolly-haired vs wooly

woolly-haired and wooly both are adjectives.

Word	Noun	Adjective	Verb	Adverb
woolly-haired	No	Yes	No	No
wooly	No	Yes	No	No

As adjectives, woolly-haired and wooly are synonyms defined as:

Other synonyms of woolly-haired include woolly, wooly-haired.

woolly-haired (adjective)	wooly (adjective)
covered with dense often matted or curly hairs	confused and vague; used especially of thinking
	covered with dense often matted or curly hairs
	having a fluffy character or appearance