You’re indoors in the sense that you’re protected from the weather and the elements, and the cave could even have some kind of covering or entrance area that could be considered a door or doorway. People have built homes in caves.
Is caving an outside, inside activity?
Do I have to walk through the door? Can there just be a door at one of the entrances?
What if I enter a cave through a door installed in a doorway, but there are other entrances that don’t have doors?
What if you enter the cave through an opening where the door isn’t but I know the cave system has a door at one of the entrances elsewhere?
If you go in the door you’re indoors but if you don’t you’re outdoor.
This could lead to a strange situation where you enter the cave through a doorless entrance and leave through an entrance with a door, making the outdoors indoors in the split second before you fade from existence.
Go outside. Enter cave. Leave cave through another opening. Open door to exit cave. Explode.
Exactly what I said just less eloquent.