If you're building your own natural language processor, you may find that the classic eight parts of speech lack a sufficient level of detail and symmetry.
Before we look at the indoors/outdoors and indoor/outdoor pairs, we should look at the more basic in/out pairing.
"In" is a preposition. At least, the average high school student is likely to label that word in that fashion. It's a sensible label. "In the box" functions as a prepositional phrase. The preposition "in" has the object "the box". The phrase can modify either a noun or a verb. In ordinary usage, the phrase follows the thing that it modifies.
If "in" is a preposition, then its antonym "out" should be a preposition as well. However, "out" doesn't behave the same as "in". "In the box" is a perfectly natural phrase. "Out the box" is not.* Literate native speakers are far more likely to contrast "in the box" with "out of the box" -- a phrase which includes yet another preposition. By itself, the word "out" doesn't evoke the same expectation of an object as "in".
One possible solution is to consider "in" to be a transitive preposition, but to consider "out" as an intransitive preposition. Although this lacks symmetry, it would allow your processor to anticipate prepositional objects in places where they are more likely to occur.
Another possible solution is to ignore the classic eight entirely. Find a brand-new way of labelling how each word functions, based on the way that the rest of your system parses text.
Either way, the indoors/outdoors pair needs some kind of label. These seem to be fused phrases, functioning similarly to "inside the door" and "outside of the door". Perhaps the indoor/outdoor pair are adjectives, but the indoors/outdoors pair are adverbs and nouns. Perhaps indoor/outdoor are leading modifiers (as in "the indoor pool") but indoors/outdoors are trailing modifiers (as in "the pool indoors").
Since you're making your own judgements about the grammatical function of each word in your dictionary, no; there's nothing that prevents you from labelling "indoors" as a noun. However, there is something that keeps you from labelling it only as a noun.
✓ Take it indoors.
✗ Take it the car.
✓ Take it to the car.
✓ Take it carefully.
The word "indoors" can modify a verb in a way that nouns on their own do not. I can't tell you whether you need to label "indoors" as an intransitive preposition, an adverb, a trailing modifier, or anything else in particular. I can only say that, if it is tagged as a noun, it must be given at least one more tag to account for this behaviour.
* Ok, "out the box" is available in certain dialects and certain registers. It's not universally rejected, but it's not universally accepted, either. On the other hand, "out the door" is perfectly natural and might be universally accepted. I have no idea** how your processor might handle this distinction.
** Well, actually I have one idea. I imagine I would render "out of the box" as an intransitive preposition modified by a prepositional phrase, and I would render "out the door" as "out [through] the door" -- an intransitive preposition followed by a prepositional phrase with an elided preposition.