hoar vs gray-headed

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

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

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

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

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

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

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