I would imagine that freezing it would alter the taste a bit, if you're a seasoned drinker and familiar with kava's taste. I say this for the same reason I don't freeze my coffee beans, because the resins inside of the bean (all of the flavor) are getting frozen in the freezer, and then when ground and prepared, the flavor is stale and a bit off as compared to coffee beans that sat in a dry opaque container out of sunlight. Now, I'm not a kava "taste" connoisseur or anything, I chug my shells to get rid of the taste quick, I'm just throwing that out there. Just for the risk of that "freezer burnt taste" that Carolina BC mentioned, I'd rather just let my kava sit in a dry cool cupboard out of sunlight or extreme temperatures. My Solomon Islands kava sat previously opened for nearly a year and I didn't notice anything different about it. Kava seems to have a pretty long shelf life.
So yeah, my two cents, would be to keep kava out of sunlight, in a dry cool place, make sure your bags are sealed and try to get as much air out of the bag as possible before storage.