Warning: SPOILERS for Dark Web: X-Men #1
A very special mutant could turn the tide in battle, but the X-Men want nothing to do with him, and haven't even invited him on the team. The mutants of Earth need all the help they can get in the aftermath of the Judgment Day event, in which Krakoa was devastated by an Eternals attack (followed shortly by a Celestial's judgment of everyone on earth). But in Dark Web: X-Men #1, despite the plight of the X-Men, they still don't want Santa Claus on their side.
Santa is not the only major public figure to be revealed as a mutant in Marvel history. Irene Adler, a famous character in Sherlock Holmes stories, was actually Destiny, a mutant who could sense the future; she currently sits on the Quiet Council of Krakoa and is in a relationship with the shapeshifting mutant Mystique. In the film X-Men: Days of Future Past, it is also heavily hinted by Magneto that former President John F. Kennedy was a mutant (and this is also alluded to in the comics, in which he is a low-level telepath who lacks the strength of Professor Xavier or Jean Grey).
In Dark Web: X-Men #1, written by Gerry Duggan with art by Rod Reis, the entire city of New York is affected by the spells presented in the Dark Web event, and inanimate objects spontaneously begin to grow teeth - most notably the Rockefeller Christmas Tree. Spider-Man, Jean Grey, Cyclops and several other X-Men eventually save the city, but cannot avoid property damage and the poor optics of "ruining Christmas." A young bystander who saw the tree eat a Santa impersonator is comforted by Spider-Man: "Don't worry, though - he's a mutant and the X-Men are gonna resurrect him at their Keebler treehouse."
Santa Is A Mutant (And The X-Men Don't Want Him On The Team)
In the Marvel Universe, Santa is indeed a mutant, and a tremendously powerful one at that. Santa is classified as an Omega-level mutant (the same classification as Phoenix, for example), and has multiple powers, including teleportation, memory erasure, and the ability to control the weather, or at least create snow. The entire affair was depicted in 1991's Marvel Holiday Special, and as par for the course for a 90s comic, has a ridiculous premise and plot but is quite entertaining.
In a way, Santa Claus is treated the same way as Squirrel Girl is today. Both characters have tremendous power, but the inherent comedy of seeing them involve themselves in serious stories often means they are left out entirely. This unfortunately means that Santa Claus will not join the X-Men anytime soon, and perhaps that is for the best.