IIRC, recognizing people's faces is a very specialized brain activity, which seems to be only partially related to other visual skills or memory - there is even a disorder called prosopagnosia
that specifically impacts the ability to recognize faces.
I have no trouble recognizing peoples faces, but I usually find it very hard to remember their name. Also I haven't been able to learn a single dance in my life so I usually just bounce around :-)
update: I usually don't think of anything at all when I count, but when I'm distracted I do use my fingers.