wooly-haired vs wooly

wooly-haired and wooly both are adjectives.

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

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

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

wooly-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