Mozzarella doesn't freeze very well, there's too much moisture. Cheddar is a bit firmer and could hold up better.
If you decide to freeze either, don't use them as toppings you wish to brown. Instead, use them in the meal. When the cheese defrosts, the ice crystals that formed, especially in the mozzarella, alter the cheese's melting ability. It will still melt, but it browns much much faster, starting to burn before it completely melts.
How can we sleep while our beds are burning???