A
black hole only has
three characteristics one can measure from the
outside:
Mass: The mass of the black hole determines the size of its
event horizon. It also determines its gravitational pull at a given distance away from it. Thus, the mass can be measured.
Angular momentum: i.e.
spin. A black hole can spin, yes. Due to the law of conservation of angular momentum, if a spinning mass turns into a black hole, the resultant hole must still spin. Just because it's a singularity doesn't mean it can escape the basic laws of nature! (well, at least outside the event horizon).
Charge: As above, the
law of conservation of charge prevents charge from just disappearing. This means that if one found a small black hole, and shot enough
charged particles into it, the hole would acquire a charge. You could then move it around with really, really big electrically charged plates, for example. Slowly, true, but so what?
How many people could claim they had a black hole following them around?
Those are all the properties of the black hole. Thus the physicist's saying:
A black hole has no hair.