What a lovely plant!
I've looked at your plant, and my first thought was that it may be a form of Mammillaria formosa. This is a very variable species, so often photos in books or on the web don't look the same. You just have to look at M. formosa in Maurillio's Mammillarias A to Z in the Photo Section to see how much variation there is.
My second possibility is M. saetigera, which is what the Germans call the plant that I know as M. hahniana,especially ssp woodsii, having decided that M. hahniana with long hair is actually a form of M. klissingiana.
My third possibility is Mammillaria albilanata ssp. oaxacana, but I think that is a long shot.
So, not a conclusive identification from me, but I am tending towards M. formosa.