Well, Christmas is approaching, so why not include a trope related to the holidays? And why not make it about one of the most prominent figures to adherents: Santa?
Santa Claus is an extraordinarily popular holiday figurehead, the very essence of the season wrapped in a jolly, overweight package. Most know him as the bearer of gifts to good children (and coal to naughty ones), though his history is naturally wrought with cultural evolution. Below are some cultural notes on the inspirations before we dip into the personification of Christmas himself.
Santa's earliest and primary inspiration is Saint Nicholas of Myra, a 4th century bishop of Greek descent living in what is now Turkey. Saint Nicholas (who would later lend his own name to the jolly elf) devoted his life to Christianity and is commonly depicted in European art donning his bishop robes. His remains were, according to legend and relics, taken by sailors from Italy during rotating conquests of the region between the Byzantine Empire and the Seljuk Turks. His remains turned up in Bari, Italy, as a result.
Some parallels were given between Claus and Odin, a major god within Norse mythology, prior to Claus' Christianization. One such example was how children would fill boots with various foods fit for Odin's horse. Doing so would encourage Odin to repay their kindness with gifts and candy.
Beyond Odin, there is Dutch tradition, where Saint Nicholas is aided by helpers, who became Krampus (demons) in Germanic myths and friendly elves in the United States. According to tradition, they arrive by steamship from Spain containing notes on which children were naughty or nice. It's here where we see why Saint Nicholas is the most direct inspiration, although their looks differ (Saint Nicholas sported bishop's robes, as per traditional European depictions).
With the attention given to giving gifts to children, it isn't uncommon to depict Santa as a kindly gentleman, with patience of a saint. However, this isn't always the case. There are several ways to interpret the Bad Santa trope, as noted in the trope page. If it is Santa himself, he is decidedly stressed out, possibly hitting the egg nog fairly hard, and can't take it anymore. Alternatively it isn't really Santa, but an impostor that no one know is fake. Thirdly, it is a Mall Santa (hence someone we know isn't the real deal, regardless of whether Santa exists in the setting or not) and he happens to suck at his job.
As such, know how to play it appropriately when using this trope. It may not make much sense to play up the Mall Santa variety as 'potentially real' if there is no good indication he is; it can still happen, if paranoia and such are handled and used properly, but it isn't a guarantee. Establish the possibility early and with force, if so.
Also, remember the Show, Don't Tell rule: no one will believe you if your alleged Bad Santa is simple apathetic at worst. He may still be a decent Santa, just one seeing it as a job rather than a joy. Plus don't make him seem too likeable if you truly desire everyone to hate this Santa. Sometimes the wrong characterization can ruin any and all intentions.
