Freezing cheese is the best way to store it for long periods without loss of moisture. The problem with this is that the texture is sure to change, and not for the better. When taken out and defrosted, even super sharp cheddar would be flaky. Some other types would even become powdery and grainy. While this will not be an issue for cooking, it would likely ruin your plans for a separate snack. The cheese in question would not pass as a good appetizer. People usually let the cheese grow a little mold and cut this off before serving.
It is important to have cheese to be frozen, in as close as possible to the form you will be using it in later. Cheddar, even super sharp cheddar, can be frozen in blocks, but then later you would have to thaw the whole block, no matter how little want to use at the time. This can be hard to handle, particularly if you are buying in bulk.
Use suitable wrapping
If you are going to freeze sliced super sharp cheddar, the slices will need to be separated with waxed paper. This will not be necessary if you are freezing it straight from the package. It is meant to make separating the slices easier afterwards.
When freezing shredded cheddar, toss it in flour or cornstarch beforehand. This will keep the shreds from forming clumps, which would be hard to separate later.
Use a heavy-duty freezer bag or heavy aluminum foil when wrapping the cheese on the outside, and also make sure to get most of the air out before sealing.
A semi-hard cheese such as super sharp cheddar can be preserved in this way for over a couple of months. This can be stretched if you do not open the freezer very often, and have backup power to tide the fridge through a power failure. Longer than an hour outside refrigeration, and the cheese can become useless.
Freezing is actually good in one way: it makes the cheese easier to grate. Especially if you are dealing with something that has narrow ends when you place in the freezer, it will be easier to use a greater on. In fact freezing an hour beforehand is a good way to ease grating. Make sure that you do not freeze it for too long though, because there is a limit past which the cheddar will not be very edible.