Restricting to vacuum, the conserved mass and angular momentum are respectively conjugate to the timelike and rotational symmetries of the black hole. No-hair may roughly be equivalently stated as "isolated black holes do not radiate and are axisymmetric".

This is obviously not true of all black holes. For example the members of a black hole binary tidally deform one another and emit gravitational radiation, so you will need more than these parameters to describe them. Similarly, if you throw something really big into a black hole, it will wobble for a bit, which will break the symmetries. No-hair says rather these transient behaviours will be exponentially damped (i.e. a black hole has no stable ringing modes).

No-hair can be sort of thought of as an amped-up version of Birkhoff's theorem. The latter says that the Schwarzschild black hole is the unique spherically symmetric vacuum solution to general relativity. This doesn't quite put limitations on what "cosmohikers" could or could not do beneath the event horizon, because the theorem gives no reason to expect black holes to in fact by spherically symmetric. But it does imply that if you ever found a spherically symmetric black hole, it would have a conserved mass: spherically symmetric gravitational radiation is impossible, because that would constitute a spherically symmetric solution different from the Schwarzschild black hole.

Restricting to vacuum, the conserved mass and angular momentum are respectively conjugate to the timelike and rotational symmetries of the black hole. No-hair may roughly be equivalently stated as "isolated black holes do not radiate and are axisymmetric".

This is obviously not true of all black holes. For example the members of a black hole binary tidally deform one another and emit gravitational radiation, so you will need more than these parameters to describe them. Similarly, if you throw something really big into a black hole, it will wobble for a bit, which will break the symmetries. No-hair says rather these transient behaviours will be exponentially damped (i.e. a black hole has no stable ringing modes).

No-hair can be sort of thought of as an amped-up version of Birkhoff's theorem. The latter says that the Schwarzschild black hole is the unique spherically symmetric vacuum solution to general relativity. This doesn't quite put limitations on what "cosmohikers" could or could not do beneath the event horizon, because the theorem gives no reason to expect black holes to in fact be spherically symmetric. But it does imply that if you ever found a spherically symmetric black hole, it would have a conserved mass: spherically symmetric gravitational radiation is impossible, because that would constitute a spherically symmetric solution different from the Schwarzschild black hole.