out-of-doors vs open air

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

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

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

Other synonyms of out-of-doors include open, outdoors.

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