Depends on the cheese, and on the usage, really. My mom works at a cheese factory, so I regularly get more cheese than I know what to do with, so most of it ends up in the freezer. Non-aged cheese (not familiar with the English terminology, sorry) is absolutely no problem to freeze in my experience. Aged cheese, at least the ones I eat, crumbles completely after defrosting, absolutely impossible to slice - but I only use aged cheese for pizza and other stuff that goes into the oven, so the fact that it falls apart just by touching it is more of a feature for me - no need to grate it!