There are many common misconceptions regarding the enzymes in your food -- whether they're useful to you and what affects them. In very simple terms, freezing doesn't kill enzymes in food for two reasons. First, they're not alive, so they can't be killed. Second, freezing doesn't permanently affect enzyme structure.
Enzymes aren't living things, meaning that no matter what you do to them, you can't kill them. Instead, they're proteins, explain Drs. Reginald Garrett and Charles Grisham in their book "Biochemistry." They play important roles in all living organisms, as they help cells to engage in necessary chemical reactions. For instance, your digestive tract depends upon enzymes produced by digestive tract cells to break down nutrient molecules in your food. Other body cells use different enzymes to build products and engage in other cellular reactions.
Effect of Freezing
There are some things that destroy enzymes. Exposing them to very high levels of acidity and exposing them to heat, for instance, causes denaturation. When an enzyme is denatured, it loses its shape, rendering it nonfunctional. Freezing an enzyme has a different effect, however. Rather than denaturing the enzyme, freezing appears simply to slow the rate at which the enzyme operates. There is no permanent effect on enzyme function as a result of freezing, explain Dr. A. Meijer and colleagues in a 1977 article in "Histochemistry and Cell Biology."
Uses of Enzymes
Despite the fact that your cells depend upon enzymes to digest food and perform many other functions, your cells make their own enzymes. There's no scientific evidence to suggest that they need -- or even have a mechanism for utilizing -- enzymes from food or other supplemental sources. As such, though you can rest assured that freezing won't affect the enzymes in your food, it wouldn't matter if it did.
One of the very few supplemental enzymes that humans appear to benefit from in certain cases is lactase, the enzyme that digests milk sugar. Some individuals don't produce sufficient lactase to digest dairy, resulting in lactose intolerance. If you're lactose intolerant, you can take supplemental lactase to provide you with the temporary ability to digest lactose. Lactase activity isn't affected by freezing, meaning that even frozen sources of lactase still allow you to digest milk sugar.