Store any leftover cinnamon rolls in an airtight container in the fridge. They will keep for about 1 week. You can freeze sourdough cinnamon buns for up to 3 months, but only after baking, and before spreading icing on them. Powdered sugar cinnamon roll icing only takes 5 minutes to make, so it's best to wait and ice the rolls after they have thawed out. We suggest doing this just before you serve them.