The more that I reflect on this little song the more it is clear to me how it functions like a short understanding of Rene Girard's theory of Mimetic desire and sacred violence. Take a look at each section of the song:
Rudolph the Red-Nosed Reindeer had a very shiny nose. And if you ever saw it you would even say it glows. All of the other reindeer, used to laugh and call him names. They never let poor Rudolph join in any reindeer games.
Notice that Rudolph is identified by what makes him different and odd. Just like any scapegoat is a deemed odd by the group. Also notice the power of the mob and how the mob seeks to justify its action - if you ever saw how weird this guy was you too would do what the group would do. The oddity of the victim makes him the butt of jokes and further ostracizing. Additionally the victim is never allowed to be a part of the "normal" group/mob's games. This sets Rudolf up as a ready scapegoat when a need arises.
Then there is a crisis, or a scandal:
Then one foggy Christmas Eve, Santa came to say, "Rudolph, with your nose so bright, Won't you guide my sleigh tonight?"
With any crisis, the community needs resolution or, as Girard says, "the social fabric will burst". So the mob uses a scapegoat to ease the crisis. In this case, the crisis is set and so they put Rudolph in the lead position, so that if anything goes wrong, we can all blame Rudolph and his obvious inability to lead or be a contributing member of the community. Also it is worth noting that our imaginations have several reindeer pulling the sleigh, the song can also suggest that there is only one reindeer pulling the sleigh, and in the time of great crisis and most danger the one selected is the "odd one" who will not be missed if unsuccessful.
With little choice, Rudolph leads the sleigh and we hold our breath to see if the would be scapegoat dies or lives. The next part of the song is a little fuzzy on it's timeline:
Then all the reindeer loved him, as they shouted out with glee! Rudolph the red-nose Reindeer, you'll go down in history!
This line is often understood as "the end" of the story, after Santa's delivery on the sligh. But it could just as easily be read as before the foggy night delivery. As soon as the scapegoat is selected, there are shouts of great joy. And when the scapegoat is selected, the community begins to further justify the decision to scapegoat the victim - there is a promise that the scapegoat will "go down in history". Tales will be told of all the "Great Rudolph" and how he was able to quell the crisis. This happens with Presidents of the U.S.A as well. No matter what the approval rating of the president in the moment, once out of office many people have a idealized memory of them (Regan, Bush, Clinton, etc.).
Truth be told, we do not know the fate of Rudolph. Did he succeed in guiding the sleigh? We don't know from the song. The only thing we do know is that since Rudolph's time there has never been another foggy night/crisis on Christmas Eve again. And because Rudolph brought about the end of all future foggy night/crisis, Rudolph is recalled as the greatest reindeer of all. As the beginning of this morbid tale suggests:
You know Dasher and Dancer and Prancer and Vixen; Comet and Cupid and Donder and Blitzen, but do you recall the most famous reindeer of all?
I am not trying to be a downer this season. And I could totally be way wrong on this interpretation. The reason I point this all out is to highlight that it is very easy to whitewash a story that could be very tragic and make it seem like the mob was in the right the whole time. The Gospels make it clear that the mob is actually the one that is constantly wrong.
This is what makes, in part, the Gospels different from other myths, legends, tales and fables.