Just a quick note for thosde of you who know Rudolph through the song, or the song and the Rankin-Bass special alone – in the original book (which preceded the song), and in the 1940s Fleischer/Famous Studios cartoon made from it (betcha didn’t know about that one) Rudolph is not a member of the family of Santa’s reindeer!
Santa is out delivering the presents around the world and having difficulty in that snowstorm, and he gets to Rudloph’s house (Rudolph’s family unaccountably lives in a middle-class human-type house) and notices the glow from Rudolph’s nose. He wakes the reindeer kid up and asks him to help out. Rudolph is thus a stranger to the classic team of eight. A ringer. Apparently any reindeer can fly if they put their minds to it, or Santa sprinkles them with pixie dust, or whatever.
So the mean reindeer that wouldn’t let him join in the games weren’t Santa’s team or their families. At least until Rank and Base made that 1960s animation.