Sorta. Anything fatty tends to pick up flavors from the environment. Now, in the cold, those chemical reactions are slowed down, but they’re not stopped. If you leave it there for a while, it’ll pick up off flavors. Still generally safe to eat, but you won’t like it.
How airtight is airtight? Cheap Ziploc bags or Tupperware won’t be enough in the long run. Maybe if you used a pressure sealed preservatives jar. Those will need to be heated up in a pressure cooker, so butter will melt and reconstitute.