One of the main holidays celebrated in Rowling's Wizarding World (as in the Muggle World) is Christmas. Like at any other school, the Hogwarts students have Christmas holidays. Most of them go home to celebrate with their families; for those who remain at the school over the holidays, there are also Christmas celebrations held there. Christmas is included in each and every one of the seven books in the series; and the word Christmas is always used - there is no attempt made to replace it with some kind of alternative winter solstice feast. There are Christmas trees, and Christmas gifts, and Christmas dinner, and carols are sung - a bit spookily, even by empty armours!
Except for the mentioning of carols, though, there is really no suggestion of Christmas being a religious celebration. Some readers take this to mean that it is only used to mark the time of year, and that this means that the Wizarding world is a wholly secular world that does not involve any ideas of religion at all. Others, like me, see it a bit differently: I think one reason Rowling does not introduce a separate mythology in her books is that she uses the idea of the wizarding world as an image of spiritual power, and really borrows a lot from Christian and Biblical context. The Wizarding World is not separate from the Muggle world; Muggles just can't see and don't believe in Magic, just as atheists do not believe in the existence or power of a spiritual world.
There is no mentioning of a Father Christmas either in the celebrations of the Wizarding World; but then all Hogwarts students are over 11 years old, so can be supposed to have outgrown that. However... In the first book, Rowling manages to sneak in a nod at the Father Christmas/Santa Claus/St Nicholas tradition anyway: It is at Christmas time that Harry, Hermione and Ron are trying to find out the secret of who Nicolas Flamel is.
"They had indeed been searching books for Flamel's name ever since Hagrid had let it slip, because how else were they going to find out what Snape was trying to steal?" (Philosopher's Stone, Ch 12)
Of course in history, St Nicholas and Nicolas Flamel were different persons, living in different centuries. However, according to traditions, they had at least two qualities in common: They both performed "miracles", and they both gave a lot to charity.
Saint Nicholas is the common name for Nicholas of Myra (270 - 346), a saint and Bishop of Myra (Demre, in Lycia, part of modern-day Turkey). Because of the many miracles attributed to his intercession, he is also known as Nicholas the Wonderworker. He had a reputation for secret gift-giving, such as putting coins in the shoes of those who left them out for him, and thus became the model for Santa Claus. (From Wikipedia article about St Nicholas)
Nicolas Flamel (1330-1418) was a successful French scrivener and manuscript-seller who developed a posthumous reputation as an alchemist due to his reputed work on the philosopher's stone. The essence of his reputation is that he succeeded at the two magical goals of alchemy: that he made the Philosopher's Stone which turns lead into gold, and that he and his wife Perenelle achieved immortality. Flamel's death was recorded in 1418, but his tomb is empty. Rumors spread that Nicolas Flamel never actually died, since witnesses claimed to have seen him in 1761 at an opera in Paris. It is also said that the Flamels used their enormous wealth to support churches and schools and to care for the sick and poor. (From Wikipedia articles about Nicolas Flamel and Perenelle Flamel.)
Portrait of Nicolas Flamel
from a nineteenth century engraving
from a nineteenth century engraving
Harry finally finds the name Nicolas Flamel on a Famous Wizard card that comes with a certain kind of Chocolate Frogs that can be bought in the Wizarding World:
"Professor Dumbledore is particularly famous for his defeat of the dark wizard Grindelwald in 1945, for the discovery of the twelve uses of dragon's blood and his work on alchemy with his partner Nicolas Flamel."
According to a Hogwarts library book that Hermione finds, Nicolas Flamel is "the only known maker of the philosopher's stone". Apart from transforming any metal into gold, the philospher's stone also "produces The Elixir of Life, which will make the drinker immortal".
And this is of course why the evil wizard Voldemort wants it, and must be stopped from getting it; because he certainly would not be using its powers for charity...
Also notice the word association - Flamel - flame - fire - fireplaces... In the Christmas tradition of the English-speaking world, Santa comes through the chimney. In the Harry Potter series, Fire is the element which represents Gryffindor, the house to which Harry and friends belong, and which has a reputation of bravery, and fighting for the good side. In the HP books, fireplaces are used for transportation and communication - of the good kind, while water (and toilets!) represent Slytherin, and everything sneaky and slimy. (See post from April 2009: Going to the Bathroom.)
In my opinion, Rowling does an excellent job of setting the discoveries of the secrets of Nicolas Flamel in the context of Christmas in the first book.
Neither Flamel nor the philosopher's stone survive to pass on into the following books in the series; but the alchemy theme does, although mostly in much more subtle references. Well hidden references is Rowling's speciality - in fact, a lot of them are so NOT obvious, that if you are not used to looking for them, you can read the whole series without getting any of them. Or you can spend years amusing yourself by trying to find them...!