So, it appears, are all the rest of St Nicholas's steeds and possibly the old man himself. For research by Norwegian and Danish scientists has shown that the world's reindeer are "hot" and are contaminating their owners and minders.
The radiation comes from the 500 atomic bomb tests carried out in the atmosphere by the nuclear nations in the 1950s and 1960s. Long-lived isotopes in the fall out - including Caesium 137 and Strontium 90 - have built up in Arctic lichens, which are particularly good at accumulating them.
The reindeer eat the lichens, their staple diet, and concentrate the isotopes in their bodies. Animals are affected all over the Arctic, with the most radioactive reindeer in Canada, Alaska and Siberia's Taimyr Peninsula.
Enormous amounts of reindeer meat - some 14,000 tonnes - are eaten in the Arctic each year. Research at the Danish Riso National Laboratory has found that reindeer herders, who consume a lot of the meat, take in 300 times more radiation each year than the average Briton. Norway's Radiation Protection Authority estimates that hundreds of them have died of cancer as a result.
Meanwhile reindeer are emerging as one of the greatest environmental threats to the Norwegian Arctic. Over-grazing and trampling is causing more damage to the fragile tundra than some of the world's most seriously polluting factories.
Over the last 40 years the number of reindeer in the Norwegian Arctic have doubled, reaching 20 animals per square kilometre, a very high density.
Research by the Norwegian and Finnish geological surveys and Russia's Kola Science Centre have found that 75 per cent of the moss in the Norwegian Arctic and 85 per cent of lichen have been "severely damaged" by reindeer. Three-quarters of the area is suffering from soil erosion.
By contrast, two of the world's most polluting factories - nickel smelters in Russia's Kola peninsula - have only damaged about 10 per cent of the moss and 14 per cent of the lichen in the area.
Even the Saami people, who own most of the reindeer, admit that they may be causing problems. Lars-Anders Baer, vice-president of their council, told a conference on the Arctic environment this year: "We don't know how many reindeer the northern part of Norway can take."Reuse content