In reply to Anhibian:
The surface oxidation will be inconsequential. It will brush off with your finger tips.
To care for crampons, just dry them out and store them dry. Unless you have been doing something funky with them like climbing chalk sea cliffs. In which case wash the salty sea grease off first.
The black coating is usually a polymeric powder coat, paint.
WD 40 does have quite a high water content. A rub down with an oily rag or just drying naturally is probably best.