gray-headed vs hoar

gray-headed is not a noun while hoar is a noun.

Word	Noun	Adjective	Verb	Adverb
gray-headed	No	Yes	No	No
hoar	Yes	Yes	No	No

As adjectives, gray-headed and hoar are synonyms defined as:

gray-headed and hoar: showing characteristics of age, especially having grey or white hair

Other synonyms of gray-headed include gray-haired, gray, grey-haired, grey-headed, grey, grizzly, hoary, white-haired.

gray-headed (noun)	hoar (noun)
	ice crystals forming a white deposit (especially on objects outside)

gray-headed (adjective)	hoar (adjective)
showing characteristics of age, especially having grey or white hair	showing characteristics of age, especially having grey or white hair