One paper is: “Microcirculatory investigations of nasal mucosa in reindeer Rangifer tarandus (Mammalia, Artiodactyla, Cervidae): Rudolph’s nose was overheated,” Ben van der Hoven, Eva Klijn, Michel van Genderen, Willem Schaftenaar, Lisette L. de Vogel, Ditty van Duijn and Erwin J.O. Kompanje, Deinsea, December 19, 2012, pp. 37-46.
The authors, at several institutions in Rotterdam, The Netherlands, report:
The classic Christmas tale and song ‘Rudolph the red-nosed reindeer’ evoked several theories about the cause of the remarkable colour of the animal’s nose, ranging from (1) a common cold, (2) alcoholic intoxication, to (3) a parasitic infection of the nostrils. Still, there is no conclusive scientific evidence of the nature of Rudolph’s red nose. We found a clue in earlier studies that showed reindeer are able to restrict respiratory heat loss by the use of nasal heat exchange. […] We found hairpin shaped ‘radiator-like’ (looping) small blood vessels in the nasal mucosa, which are most likely responsible for the warming and/or cooling of the inhaled freezing arctic air during nasal panting. […] The exceptional physical burden of flying with a sleigh with Santa Claus as a heavy load could have caused cerebral and bodily hyperthermia, resulting in an overworked nasal cooling mechanism that resembles an overheated cooling radiator in a car: Rudolph suffered from hyperemia of the nasal mucosa (a red nose) under more extreme heat loads during flight with a sleigh.
The other paper is: “Why Rudolph’s nose is red: observational study,” Can Ince, Anne-Marije van Kuijen, Dan M J Milstein, Koray Yürük, Lars P Folkow, Wytske J Fokkens, Arnoldus S Blix, BMJ, December 17, 2012;345:e8311.
The authors, at several institutions in Rotterdam and Amsterdam, The Netherlands, and Tromsø, Norway, report:
Similarities between human and reindeer nasal microcirculation were uncovered. Hairpin-like capillaries in the reindeers’ nasal septal mucosa were rich in red blood cells, with a perfused vessel density of 20 (SD 0.7) mm/mm2. […] The nasal microcirculation of reindeer is richly vascularised, with a vascular density 25% higher than that in humans. These results highlight the intrinsic physiological properties of Rudolph’s legendary luminous red nose, which help to protect it from freezing during sleigh rides and to regulate the temperature of the reindeer’s brain, factors essential for flying reindeer pulling Santa Claus’s sleigh under extreme temperatures.
BONUS: Figure A (from Ince et al. 2012) also reveals that Rudolph also has a red arse. This was apparently not noticed by the authors (they did not specifically mention it in their paper).