We all know that Father Christmas is originally St Nicholas- a third century Greek saint from modern Turkey, pictured by a Novgorod School medieval artist in this icon below...
This icon though still looks recognisably like Father Christmas- but this was painted centuries indeed millenia after St Nicholas died. Indeed there is no real picture of St Nicholas to be had, all the pictures we have are like this one and until the recent reconstruction of the fragments of his skull are made more exact, that's all we have. So that leaves the key question still open did Santa Claus have a beard?
Well the original models for the drawings of Father Christmas are these icons of St Nicholas and whilst we'll never know whether St Nick had a beard, its rather interesting to assess why the portraits have a beard. If you go back to when these portraits were painted, say back to the court of Ivan the Terrible in Russia, then you find Church Ordinances past against clean shaven men- why. According to Isabel de Madriaga's great biography of Ivan, there is only one reason- clean shaven men were seen as emulating women, attempting to look effeminate and as homosexual. The Church has never been too keen on what it calls the sin of Sodom and in 14th and 15th Century Russia, you'll be unsurprised tolerance of homosexuality was not at an all time high.
So it turns out that Santa Claus's beard is there for a simple reason- it signifies that he has a wife and kids back in the igloo in Lapland, and doesn't go home to the clasp of a male elf. Santa's beard is a relic of 14th Century homophobia.