Odin

Odin first appears in White Night, as Donar Vadderung, the head and CEO of Monoc Securities. He later appears in Cold Days as Kringle, or Santa Claus.

Donar Vadderung
As Vadderung, he is described as not all that imposing, though a man in good shape and in his early fifties. Lean and spare like a long distance runner only with heavy shoulders and arms. His hair is long, a bit shaggy, and the color of a "thundercloud". His one eye is ice blue with a patch over the other eye that bears a vertical scar running from above the eyebrow, through the space where the eye would be, ending at mid-cheek. His laugh is hearty, "like Santa Claus must have had when he was a young man and playing football."

The top of Monoc Securities where Harry Dresden was taken to meet Donar Vadderung is where it is said is the center of his power on Midgard. He tells Harry that he could simply wish him dead. According to Uriel, they know each other and are in similar fields. Uriel also warned Harry to consider Vadderung's words carefully.

In White Night, Harry listed him as one of the Freeholding Lords with rights under the Unseelie Accords, when telling Murphy about what it means. According to Marcone, Vadderung is the current CEO of Monoc Securities. , which is later confirmed by Gard.

Hugin and Munin are his assistants, and they do not like Harry much. Harry first met them at Monoc Securities. They appeared as receptionists, pretty, tall, and deadly.

Kringle
As Kringle, he is compared to a bear. He has broad shoulders, forearms nearly as large as his upper arms, a thick neck, a barrel chest and a huge frame. Kringle's hair is short, white, "shining clean", his beard, long, white, and cascading over his chest like a fluffy wave. His eyes are "clean, winter sky blue". He has ancient scars of white-lines on his hands and face. He wears a coat of mail, obviously made of something other than iron. His open overcoat is a rich red, trimmed in white fur and held by a black leather belt. Tucked into his belt were a pair of white-fur-trimmed black leather gloves. His jovial laughs are frequently carried over the din of the parties he regularly attends at Mab's. He enjoys a good battle every few years to keep his life engaging.

He sometimes joins the Wild Hunt with Lord Herne, the Erlking. and appears to know Sarissa and some secret about her, agreeing to remain silent about it. Dresden is a fanboy.

In Cold Days, Kringle reveals that the Winter King may be another Mantle, worn seasonally by Odin. He also stated hawthorn wood grows hot and "doesn't care for creatures of winter."

White Night
In White Night, Donar Vadderung is mentioned to be a signatory of the Unseelie Accords and he helps John Marcone become the first human Freelord of the Unseelie Accords.

Changes
In Changes, Odin is revealed to operate under the alias of Donar Vadderung, a powerful individual easily capable of laying out Dresden with a pure application of his will. He is known to test people on how well they upheld the traditions, obligations and responsibility as guest to host and vice versa. He'd reward the faithful and send a hideous demise to the miserly, callous, or cruel.

Harry visits Vadderung at Monoc Securities, led there by Gard at his invitation. Vadderung tells Harry he'll find his daughter in Chichén Itzá in a few days, about the Red Court's plan to use her as a sacrifice in Bloodline Curse. It turns out to be exactly what Harry needed for a successful recovery of his daughter. He also demonstrates his awesome power, which is the same kind of power he'll be facing against the Lords of Outer Night and there will be a dozen of them. Donar further said that Chichén Itzá is the center of their power and that they could just wish him dead that same as he could there at his center.

Near the end of Changes, he makes an appearance at the battle of Chichén Itzá with the Grey Council. He opened a Way for  them—made from green lightning and having a shimmering archway—and again later, those needing to leave. Before he goes, he gives Harry a fencing-like salute with his spear. Ebenezar says that he doesn't give recognition like that lightly.

Cold Days
In Cold Days, Harry meet him at McAnally's Pub to get counsel regarding Demonreach, the dangerous entities imprisoned underneath, their possible release and the island's eminent destruction. He names the destructive fire the Demonreach called the fail-safe that The Original Merlin put in place: "Banefire". He told Harry that should it be triggered, it would mean the end of everything. The also discussed the issue of time dimensions being involved. Harry asked if he can do it, Donar says that he can.

During the closing of Cold Days Kringle (Santa Claus) turns to Harry and winks, briefly showing the visage of Odin. He makes a statement in regard to Mantles and Masks as an explanation.

In Cold Days, Harry Dresden is first introduced to Kringle at Mab's combination birthday party and introduction party for the new Winter Knight.

Kringle was a part of the Wild Hunt during which he goes after Harry. Harry succeeds in taking him down and Kringle concedes. Harry takes over the Wild Hunt having defeated the Erlking as well. As new leader, Harry commands that they hunt Outsiders to which there is a great cheer.

Later, Kringle gave Harry a message that Mab took the new Ladies with her and Molly will be returned to apartment in a few days. Harry suggested to Kringle that he and Erlking could have taken Harry, that they meant for Harry to lead the Hunt. Kringle responded that the Hunt would not have followed him if Harry didn't take it, nobody gives command of the Hunt. Kringle advises Harry not to break Mab's pride, especially in the presence of others. Just before leaving Kringle winked at Harry. And, for the briefest instant, Harry saw Donar Vadderung's face melded with Kringle's face. Kringle sings "Here Comes Santa Clause" while walking away.

Skin Game
In Skin Game, Mab arranged a meeting between Kringle and Harry Dresden, where it was established that Kringle and Odin were the one and the same, but that legally they were to be considered two different persons, so much so, that Mab could call on Kringle without objection, but she would have had to wait in line if she had called on Vadderung. In the meeting, he and Dresden arranged for covert operative to join the mission to Hades' Vault as a plant of Dresden's.

In mythology
In mythology, Santa Claus is believed to be based on the merging of the myths of Saint Nicholas of Myra and the Legend of the Norse God Odin.

Word of Butcher
According to Jim Butcher he is kind, the spirit of generosity in a time of bleakness. Jim also said that Santa Claus is the Winter King and goes by other names and the Erlking is the Summer King, though the Erlking is not attached to any court. He added that it's more accurate to say that Kringle is "a" Winter King, rather than "the" Winter King -- that the Kings are aligned with or related to the Summer or Winter, but not parts of those Courts (from an Interview on Reddit). Additionally, the kings' characters are opposite to the court to which they associated. Kringle is kindly which is opposite to the Winter Court and the Erlking is not so friendly. (No mention of Santa Claus being a Wyldfae.)

Quotes

 * "They say you can know a man by his enemies, Dresden. You defy beings that should cow you into silence. You resist forces that are inevitable for no more reason than that you believe they should be resisted. You bow your head to neither demons nor angels, and you put yourself in harm's way to defend those who cannot defend themselves. I think I like you."

---
 * It's dawn, when Halloween officially ended...

---
 * He looked out at the lightening sky and let out a satisfied breath. "It was Halloween, Dresden. You put on a mask for a time. That's all." He looked directly at me and said. "Many many mantle are worn—or discarded—on Halloween night, wizard."

---
 * "You mean masks?" I said, frowning.
 * "Masks, mantles," Kringle said. "What's the difference?"
 * He winked at me.
 * And for the briefest fraction of a second, the shadows falling from the tower and the cottage in the gathering morning behind us seemed to flow together. The eye he winked with vanished behind a stripe of shadow and what looked like a wide scar. His face seemed leaner, and for that instant I saw Vadderung's wolfish features lurking inside Kringle's.
 * I sat straight up, staring.
 * Kringle finished his wink, turned jauntily, and started walking down the hill, singing "Here Comes Santa Claus" in a rumbling bass voice.
 * I stared after him.
 * "Son of a bitch," I muttered to myself.

---
 * "Dude. You're... freaking Santa Claus." — "Not until after Halloween. Enough is enough. I'm drawing the line." ~ Harry, shocked that Santa would join the Wild Hunt. ~ Santa Claus responding.
 * "Lad, let me tell you something here and now. None of us is what we once were. Everyone has a history. Everyone comes from somewhere. Each move toward a destination. And in a lifetime as long as mine, the road can run far and take strange windings—something I judge you know something about." He gestured at himself. "This became the tale with which you are familiar only in fairly recent times."

Speculation
During Cold Days, Kringle states that he wasn't always known as Santa Claus and that it was a relatively new change, and that he participated in hunts with The Erlking. His position in The Wildhunt is later confirmed, when his hunter's mask was pulled away to reveal Kringle as one of the leaders of The Wildhunt. As mentioned above, during the closing of Cold Days Kringle turns to Harry and winks, briefly showing the visage of Odin. He makes a statement in regard to Mantles and Masks as an explanation.

Throughout Cold Days, the mantles of the Knights, Ladies, Queens and Mothers are all mantles of power that when used slowly erode their host's sense of self, eventually blurring the lines between the bearer of the mantle and the mantle itself, often making the motivations of the bearer of the mantle identical to that of the essence of the mantle itself. That said, much has also been said of the power of free will for those mortals and entities of deep conviction to retain their individual aspects of self. At the close of Cold Days, Mab admits that she was once mortal and could make choices. It could be argued that her inability to act against Maeve was an extension of Mab's separation from the mantle of Queen. Donar Vadderung/Odin/Kringle etc. hints that a mantle and masks have very little functional difference in regard to the heart or motivations of the entity itself, and by his very existence suggests that mantles, masks, and aliases can be assumed, taken up, or discarded based on choice. Who Donar Vadderung really is most likely a mystery. One could argue that the Odin alias might not be the base entity but rather just another mask or mantle. Who or whatever the entity truly is might be described more effectively by their motivations. As such, the being appears to work in mysterious ways, seems to care for mortals enough to get involved, and is an advocate for free will. One thing remains fairly clear, the entity that is known as Donar Vadderung, is adept at taking up, and setting aside mantles of power and may be an example of an entity that uses his mantles as tools rather than the mantle using "Him". This might mean that entities not defined as "mortal" can use elements of free will, or that this entity is in fact mortal. Perhaps the example of Donar Vadderung may serve as an element of hope that those who have to deal with the influence of a mantle of power may retain their free will.