out-of-doors vs exterior

out-of-doors and exterior both are nouns.

Word	Noun	Adjective	Verb	Adverb
out-of-doors	Yes	No	No	No
exterior	Yes	Yes	No	No

As nouns, exterior is a hypernym of out-of-doors; that is, exterior is a word with a broader meaning than out-of-doors:

Other hypernyms of out-of-doors include outside.

out-of-doors (noun)	exterior (noun)
where the air is unconfined	the outer side or surface of something
	the region that is outside of something

out-of-doors (adjective)	exterior (adjective)
	situated in or suitable for the outdoors or outside of a building