Yes and no, each dairy product is a bit different:
Milk can be frozen, but it is not preferred. Freezing changes the texture and appearance of milk. Freezing milk does not harm the milk but disturbs the quality in taste and consistency.
Cheese can be frozen, but it may become mealy and crumbly when thawed. Thawed cheese is best used crumbled or shredded in salads, as toppings or in cooked dishes. Some cheeses are better frozen than others. Because blue cheese varieties like Roquefort and Gorgonzola are generally used crumbled, further change in their texture is of little consequence. Because other cheeses like Parmesan and Romano can be stored in the refrigerator for prolonged periods, freezing is unnecessary.
When freezing cheese, freeze quickly and store at 0º F or lower. Thaw in the refrigerator and use as soon as possible after thawing.
Find more instructions on freezing dairy foods here.