I put the tape on the holes and it quit, I removed the tape, and it was squealing within 10 minutes, I put the tape back on, and it hasn't done it since.
As I posted earlier, I'm going to get magnetic calenders/signs, and use them in the wintertime.
They make magnetic vinyl covers for home heat registers, which would be about the right size. (Home Depot has them).
You could also use aluminum foil tape. That's what we use on aircraft. It can be applied in cold weather, and removes cleanly and fairly easily. (I usually leave one edge folded over, to give you a tab to pull it off by). A little heat from a heat gun makes it come off even easier.