I'm really surprised that people DON'T already freeze cheese (and butter). Thought everyone did, LOL!
I do not freeze good cheese - just the cheap stuff like American cheese slices, cheddar, shredded, etc. We've always bought the huge bag of shredded Mild Cheddar at Costco and freeze it in gallon freezer bags. We use a lot of cheese but with only 2 of us, we can't eat that much before it goes bad.