Should a Pound Cake be stored in the fridge or the freezer?
This is going to depend on how long you want to keep it for. If you're serving it soon (say, same day, maybe next), then don't refrigerate it at all, though some people seem to think it gives better flavor to refrigerate overnight.

If you've used e.g., buttercream frosting, you'll need to refrigerate or freeze it, unless you're serving immediately after frosting. Some fillings may also require refrigeration.

If you're storing short term, up to maybe a week, refrigerate it.

If you're going to be storing it long-term (more than a few days, up to three months), you'll need to tightly wrap it once its cooled, and freeze it. After more than 3–4 months, flavor will be lost, but it'll still be safe to eat, as long as its stayed at 0°F/-17°C or below.