I bookmarked this when this was originally posted, intending on giving an answer soon because I happened to have one in the freezer, but I forgot!
Now to answer over a month later, I think it tastes/'feels' just fine after freezing. I was too impatient to let it thaw by itself, so I tossed it (mozzarella) in the microwave for a minute (after making sure the metal clasp thingys are removed), and it was just fine. Not sure how long would be acceptable. I had that one in there for almost 2 months or somewhere around there (I also had it open for a while and sitting in the fridge for a few days beforehand).
So I guess for future reference, I think it's fine to freeze them.