Odin is well-known for his many bynames and, interestingly, one of them—Jólnir—specifically associates him with Yule.
Jólnir (YOLE-neer) is hard to translate. "Yule-man"? "Yule One"? "He of Yule"? "Yule-er"?
The title clearly derives from Jól, Yule. -Nir is an Old Norse suffix of agency. An English equivalent would be -er, but unlike -er, which attaches to verbs, -nir pairs with nouns. Interestingly, it is a common element in Old Norse name-creation:
Sleipnir, Odin's eight-legged horse = “slip-er,"
Skírnir, Frey's attendant = “shine-r,”
Gleipnir, the chain that bound Fenris-wolf = “open-er,”
Grímnir, another title of Odin = “mask-er” (or “hood-er”), and, of course, mostly famously of all,
Mjöllnir, the name of Thor's Hammer: “mill-er.”
So maybe “Yuler” would be the most accurate translation, though it's hard not to think of the German Weihenachtsmann, the “Yule Man.” (Modern German pagans have taken to calling Yule Weihenacht—which is an older form of the word—to differentiate it from Weihnacht, “Christmas.”)
Interestingly, Jólnir also occurs in the plural—Jólnar—for the gods generally. Rather than raising any particular theological associations, this would seem to be a convention of skaldic verse whereby the name of any particular god or goddess can poetically substitute for any other divine name (e.g. Hanga-Týr, “Hanged Tyr” for “Odin.”)
Why the specific association of Odin with Yule? In his invaluable Dictionary of Northern Mythology, Rudolf Simek suggests two possibilities. As god of the dead, Odin may be associated with the Midwinter veneration of the ancestors, or possibly the association may be due to his role as lord of the Wild Hunt, which rides the skies during the Thirteen Nights (180-1).
Here's hoping the Yule Man's good to you, wherever you are.
Rudolf Simek (1993) Dictionary of Northern Mythology (tr. Angela Hall), D. S. Brewer
Peter Nicolai Arbo, The Wild Hunt of Odin (1868)
For C. S.,
Odinsman or not