The myths and stories of Santa Claus - or Father Christmas - vary from country to country but have combined and melded over the years as culture disseminates through media exposure. Christian legends about Nicholas, the 4th Century bishop of Myra in present day Turkey being a generous gift-giver forms some of the basis. His feast day was the 6th of Dec and medieval Christians celebrated the eve of his day with gift-giving. During the 15th C reformation the celebration of saints was curtailed and instead the popular gift-giving was moved to the eve of Christ's birthday on the 25th. In Holland, the gift-giver was 'Sinterklaas' and this has remained popular, with a differentiation between him and 'de Kerstman' (The Christmas Man) as they call our familiar Santa. In England, during the reformation, it was the spirit of Father Christmas that became popular and he is synonymous with Santa Claus in the English speaking world but they are separated in other cultures.
Other myths and legends were absorbed from pagan ideas - The Germanic God Woden often visited mortals via their chimney or fire-hole and the white-bearded, hooded man visited poor households bringing gifts during the darkest winter nights. Odin was said to ride across the sky on an 8-legged reindeer. Many of these ideas swirled around European cultures for centuries but it was not until the advent of mass literacy that the more familiar tropes became fixed. In the 1820's the poem The Night Before Christmas was published. This mentioned the reindeer (and named them) and described St Nicholas as "chubby and plump, a right jolly old elf" with "a little round belly", that "shook when he laughed like a bowlful of jelly". Various 19th C American cartoonists and writers added details like living at the North Pole and wearing red - before then the character often wore green.
In the 20th C, the character continued to evolve and spread to non-English speaking and non-christian countries through movies, books and even advertising. The myth that Coca Cola somehow invented or fixed the image of Santa Claus and that they were the first to depict him in red is untrue. His image had been used for advertisers long before Coca Cola. There is often discussion in skeptic circles whether we should debunk the lie of Father Christmas's existence to credulous children or whether we should go along with the wonder of childhood innocence and use it as a skeptical teaching tool for kids as they grow up and face reality. Whatever side of the the argument you are on, we at Edinburgh Skeptics wish all of you a very merry Christmas. Ho Ho Ho! Now go listen to the best Christmas song ever: