Horse Manure.
The Santa Clause myth is not globally narrowly defined. For a start he is called various different names, Santa Claus, Father Christmas, St. Nicholas and Kris Kringle. In France, he is called Papa Noel and rides a donkey called 'Gui'. Italy have 'Le Bafana' who is more of a witch-like character and a woman. In Iceland they have the 'Yulemen', 13 mischievous dwarves who vary from gift-givers to kidnappers. Scandinavia have the 'Tomte' who are generally kind gnomish people that attack people who weren't good stewards of farmland. Russians tell their children about Ded Moroz, a traditional Santa looking fellow who has a horse driven sledge instead of a reindeer powered one, and 'Sinterklaas' is the Dutch version of Father Christmas who most resembles the popularised American version but instead comes from to the Netherlands in late November from Spain.
So no, the concept of a Christmas dwelling character isn't narrowly defined and has many different interpretations. If anything, I'd argue that you'd get a more aligned definition of 'God' if you traveled the world conducting a poll than you would with Santa.