roll in the hay vs copulate

roll in the hay is a noun but copulate is not a noun.

Word	Noun	Adjective	Verb	Adverb
roll in the hay	Yes	No	Yes	No
copulate	No	No	Yes	No

As verbs, copulate is a hypernym of roll in the hay; that is, copulate is a word with a broader meaning than roll in the hay:

Other hypernyms of roll in the hay include couple, mate, pair.

roll in the hay (noun)	copulate (noun)
slang for sexual intercourse

roll in the hay (verb)	copulate (verb)
have sexual intercourse with	engage in sexual intercourse