It's the blood vessels in the nose!

..Scandinavian scientists have found that, though it may not glow in the dark, Rudolph's nose is most definitely red. In a study published in the British Medical Journal, Dr. Can Ince of Erasmus University Rotterdam in Netherlands and his team found that a reindeer's nose is 25 percent richer in blood vessels than humans'. And after several treadmill tests, the team observed that reindeer do indeed have red noses due to increased blood circulation within their nose tissues.

Hat tip to Boinky at http://fkclinic.blogspot.com/2012/12/factoid-of-day_20.html

Here is one of my boyhood heroes singing about it.