Good old Santa Claus: in some works, he clearly exists. In fact, sometimes, he's in danger and Saving Christmas might be in order. In other works, he doesn't exist; the parents buy the presents, or maybe Christmas doesn't even exist. And then, there are these works.
In these works, Santa's existence is unclear. Mall Santas might be seen, people might try to prove or disprove Santa's existence, and sometimes evidence leans one way or the other, but we'll never know for sure.
A common way to play this trope is to introduce an old man who looks like Santa, acts like Santa, and/or claims he is Santa, but it's never proven or disproven. Sometimes, there's a reveal that someone was pretending to be Santa and there's a separate possible Santa, but he's never revealed to be Santa or not.
What is not this trope, however, is when the mysterious old man is seen with elves, flying reindeer, or anything else along those lines, as that basically proves that he's Santa, and Santa Claus is Real After All.
Additionally, don't list examples where Santa is not brought up in an important way because there are too many works like that for it to qualify.
Sub-Trope of Ambiguous Situation and Maybe Magic, Maybe Mundane. Compare Angel Unaware for another subtrope of those two tropes that might involve Christmas. Compare and contrast Yes, Virginia and Santa's Existence Clause where it is less ambiguous and Santa does exist.
- In the BBC 2018 special Click And Collect, the protagonists give ten pounds to a fat, old, homeless man with a white beard. He later comes back and gives them change for a claw machine and they wonder if he's Santa, but decide he isn't when they see him pee on a lamppost. Previously, a house's Christmas decorations featured a peeing Santa.
- Diary of a Wimpy Kid: Unlike the web comic, where Santa explicitly does not exist, in the books it is more ambiguous. Greg does not believe in Santa, but he's often wrong about things. There's a doll named Santa's Scout that's supposed to report back to Santa and it changes position, but nobody sees it move and Greg suspects it's actually Rodrick who moves it.
- The Dilly The Dinosaur story "Dilly and the Book of Bad Behavior" has Santa's prehistoric equivalent Dino Claus. His existence is ambiguous; he appears at the mall, but that might just be the equivalent of a mall Santa, and this Dino Claus needs to be informed about Dilly's situation.
- How the Grinch Stole Christmas!: The Grinch pulls a reverse Santa in order to steal Christmas, then brings it back while still in his Santa garb, but he never bumps into either the real Santa or a parent being Santa, so Santa's existence is left up in the air (in the Ron Howard live-action film version, however, not only does Santa exists but the Grinch makes his move after he watches him leave Whoville. He even makes a Deadpan Snarker joke about how Santa's lifestyle must be good for tax-dodging).
- Murdoch Mysteries: In "A Merry Murdoch Christmas", an old man is very adamant about being released from police custody because according to him, he's actually Kris Kringle and needs to complete his Christmas present rounds. Dr. Ogden thinks he's just delusional, although she consents to releasing him on the basis that he isn't putting himself or anyone else in danger. At the end of the episode, the policemen are giving the local kids gifts and notice that they have more presents than they bought themselves, upon which they notice "Kris" in the crowd, wearing a Santa suit and smiling. The man then disappears into the streets, leaving his real identity a mystery.
- St. Elsewhere: In "Santa Claus is Dead", the man whom Katherine Auschlander hired to play Santa Claus for the children at St. Eligius is hinted to be the genuine article. He knows Luther and Ehrlich by name and is aware of details of their personal lives. He also asks after the Craigs' newborn granddaughter Barbara. Luther suspects that he sent a front man ahead of him to find out all of this. The Auschlanders' grandson Max asks him to replace Katherine's snowglobe, which he broke while playing ball in the house. Although Santa Claus goes into cardiac arrest and dies immediately afterwards, Katherine nevertheless receives a snowglobe identical to the broken one with a card featuring Santa Claus' name. Dr. Auschlander denies having bought it for her.
- Arthur: In "Arthur's Perfect Christmas", there is a lot of discussion about Santa, but at the same time, it's heavily implied that the mom was the one looking for a "Tina the Talking Tabby" toy for D.W. However, it is never revealed where the kids' other presents came from, so the possibility of Santa existing is left open-ended.
- Bojack Horse Man: Parodied in the Christmas Special "Sabrina's Christmas Wish". The Show Within a Show "Horsin' Around" uses this trope and Todd asks if Santa is real. Bojack replies, "What? I dunno, we were all on cocaine."
- In The Loud House episode "11 Louds a Leapin'", Lisa does an equation that supposedly proves the non-existence of Santa, but then she thinks she's seen Santa. However, that was just their neighbor Mr. Grouse dressed up. Santa's existence is not outright denied, though.
- Postman Pat: In "Postman Pat's Magic Christmas", there is a strange old man who gives the kids presents and occasionally seems to use magic, but he's never directly stated to be Santa.