woolly vs woolly-haired

woolly and woolly-haired both are adjectives.

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

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

woolly and woolly-haired: covered with dense often matted or curly hairs

Other synonyms of woolly include wooly-haired, wooly.

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