three year old vs three-year-old horse

three year old and three-year-old horse both are nouns.

Word	Noun	Adjective	Verb	Adverb
three year old	Yes	No	No	No
three-year-old horse	Yes	No	No	No

As nouns, three year old and three-year-old horse are synonyms defined as:

three year old and three-year-old horse: a racehorse that is three years old

three year old (noun)	three-year-old horse (noun)
a racehorse that is three years old	a racehorse that is three years old