Yes, Shmuel, it will withstand dry cold OK. I'm not sure exactly your climate, but in UK, I keep my plants dry from early October until early March, temperature minimum 7C in my greenhouse.
Classifications are always changing, I'm afraid, and they depend very much on the attitude of the botanist creating the list as to how significant differences are, and whether the common characters overcome any differences. It is a judgement thing, and has raised a lot of heated debate. Most of this is, I believe a total waste of time.
My approach is that I choose one classification around which I organise my collection. But I do recognise that a plant named as X may also be called Y in someone else's classification.
An example of this could be Mammillaria magnimamma. One classification (Hunt) has this as a single very variable species. Another (Reppenhagen) uses the name magnimamma for a specific form, and uses other names, such as bucareliensis, vallensis, .... for other forms of what Hunt would simply call M. magnimamma.
I'm no botanist, so really cant tell who is right or wrong, if anyone is, so I label my plant as Mammillaria magnimamma 'bucareliensis', ideally with some field number to denote who found it and where it came from. I think that's called covering all bases!
Classifications can be found usually in pdf form on the AfM website and on the UK Mammillaria Society website.