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?
I’ve been in show caves in Bonaire that had some degree of climate control, mainly for humidity and to ensure sufficient oxygen for visitors for a comfortable experience and to accommodate large groups.
Certainly that’s the exception rather than the rule in my case.