open air vs out-of-doors

open air and out-of-doors both are nouns.

Word	Noun	Adjective	Verb	Adverb
open air	Yes	No	No	No
out-of-doors	Yes	No	No	No

As nouns, open air and out-of-doors are synonyms defined as:

Other synonyms of open air include open, outdoors.

open air (noun)	out-of-doors (noun)
where the air is unconfined	where the air is unconfined