You're not wrong about the reindeer being left out, but I think the reason why is pretty obvious. Reindeer are pretty common in the North Pole, so they probably don't stand out as much as the elves, who are a much more unique and special species. Plus, reindeer are known for pulling Santa's sleigh and delivering presents, so it's only natural that they would be given less attention than the elves, who are responsible for making all the toys and wrapping the gifts.