In The Santa Clause, Scott Calvin and his son are first introduced to the previous Santa's reindeer while they are on the roof. There are 8 reindeer. Dasher, Dancer, Prancer, Vixen, Comet, Cupid, Donner and Blitzen.
These are the reindeer names from the poem "The Night Before Christmas".
They are based on those used in the 1823 poem "A Visit from St. Nicholas" (commonly called "The Night Before Christmas"), arguably the basis of the reindeers' popularity.
Rudolph the red-nosed reindeer has become one of the most popular reindeer due to the song about him as well as the popular Christmas special that airs every Christmas in the United States. Rudolph has become part of Santa's reindeer in popular culture.
The enduring popularity of the Christmas song "Rudolph the Red-Nosed Reindeer" has led to Rudolph often joining the list, bringing the number of Santa Claus's reindeer up to nine.
Why wasn't Rudolph included with Santa's reindeer in the film? Scott Calvin even makes a reference to Rudolph while passing by Comet.
Is there some sort of trademark on the likeness of Rudolph that Disney couldn't use?