My Old Lady Cactus (Mammillaria hahniana) specimen has shorter white "hair" than many that I've seen. Some older specimens have hair that is three inches long and sticking straight out like some wild thing. The fine hair is actually modified spines, which serve to protect the cactus surface from the harsh sun. The whiteness is to reflect the sun. Maybe my cactus has shorter hair because I keep it in a lightly shaded area in the summer. It may be a little too shady, so I'm going to acclimate it to more sun, and see what happens.
The M. hahniana, a Mexico native, is an endangered species there and can’t be moved. Commercial growers propagate it with seed, so there is no shortage in this country. It is one of the easiest species to grow; therefore, it's one of the most popular, especially with kids. It seems every garden center always has a few.
In the spring, small, purple-red flowers grow in a ring near the top of the cactus. The remnants of flowers from this past spring, and even earlier springs, are clearly visible on my specimen. Next spring, the ring will be higher up, as the flowers develop on new growth.