I like the supporting evidence in this analysis from Hile Rutledge, OKA, Inc.:
Picturing the late 20th century, pop culture, largely marketing driven image of Santa that is most prevalent today, these would be the preferences I see:
Temperament of Santa - I can see the argument for NF. Santa is a poster child for personable and touchy-feely, right? But I would argue Santa is an SJ. Look at this man's project management skills. Toys for everyone in the world delivered all in one night: on time and under budget? Come on, only an SJ could pull that one off. Besides he makes a list and checks it twice. NFJs may make the list, but check it twice? Never. Santa's an SJ.
Extravert - Most of the shows and images we see of Santa show a gregarious and expressive man, frequently in the company of others. Can you imagine the network that that man must have? No Introvert would have such a thing unless he lived in total stress - and that jolly old elf certainly has a stress-free life 51 weeks out of the year.
Feeler - Santa has to be a Feeling decider. Don't be fooled by the naughty and nice list. That is not an objective, logical decision process. Fs can and do make the naughty or nice conclusion. But really, have you ever seen data that suggest that anyone has ever made it to the naughty list? There were many years that I deserved switches and coal, but I got the G.I. Joe with the Kung Fu Grip instead. Santa has shown more mercy than justice in my view. Santa is an F - a dominant Extraverted F, in fact.
I would argue that Santa is an ESFJ, which we refer to as Host/Hostess of the World, also known as the ambassadors of the world. How perfect for Father Christmas.