Can you freeze cheddar cheese?
Yes, you can freeze cheddar cheese
Best quality within 6 months, depending on the kind.

Where these times come from. USDA FoodKeeper has no entry named "cheddar cheese". The 2 kinds on this page are the USDA entries that cover cheddar cheese, copied without change from Cheese. Each row in the table is one USDA entry; pick the one that matches what you have.
block
Up to 6 months
shredded
Up to 3 to 4 months
What the freezer time means
Freezer times from USDA FoodKeeper are about quality, not safety. Food kept frozen at 0 F (-18 C) stays safe indefinitely; what changes over the months is texture, moisture and flavour. Wrap cheddar cheese tightly, press out air, and label the pack with the date so the window above is easy to track.
Thaw in the fridge, not on the counter. Anything that thawed in the fridge can be refrozen, with some further loss of quality; anything left at room temperature for more than 2 hours should not go back in.
Storage habits that make the difference
Keep dairy and eggs in the coldest part of the fridge, not the door, at 40 F (4 C) or below. Store eggs in their original carton to protect them and track the date. Reseal cheese tightly in wax paper or a container, and keep milk capped between pours.
Can you freeze other dairy products & eggs?
Source: USDA FSIS FoodKeeper dataset (public domain). How we decode the data.