When you catch a cold, your nose gets all red. Rudolph has a red nose which signals to the other reindeer that he's sick. We live in times where having any symptom, even those of the common cold might mean you have covid. So the other deer put on masks to be safe. There, that's the joke, they think Rudolph is sick because his nose is red. I guess the connection between red noses and illness isn't as well known as I had assumed it to be.

To the notes: