Cheddar Cheese when frozen will remain safe to eat and I would only recommend freezing Cheddar Cheese or any other types of cheese if you only plan to use it for cooking where you won't notice the difference in taste or texture but you can still eat Cheddar Cheese and other Cheeses that you've frozen but don't expect a good taste from it.
I would just refrigerate the Cheddar Cheese unless you're just gonna use it to cook with.
When Cheese is frozen it very often takes on a more crumbly texture and also loses some of its flavor when thawed.