Is Santa a form of Odin? Yes and No
We cannot overlook the other known influence of Santa, Saint Nicholas. Especially since yours truly was born on Saint Nicholas Day, but Saint Nicholas was born during the third century and did not have gift-making elves nor could he fly through the sky.
Many of today's popular holiday traditions stem back to pagan traditions, the trees you decorate, the wreaths you hang on the front door, kissing under the mistletoe? Yep, all pagan. They came primarily from two festivals, the Roman pagan festival Saturnalia (December 17th-24th) and the more popular Germanic festival known as Yule, a 12-day festival that lasts from December 21st-January 1st. The Yule festival included the celebration of Odin's Great Hunt in which he flew through the night sky on a magical horse named Sleipnir.
What is less freaky, eight tiny reindeer or an eight-legged horse? This fearsome creature was Odin's ride, Sleipnir. With that many legs, you might be able to fly through the sky, too. He wasn't the only Norse deity to have the ability to fly through the sky via an animal; Freya rode in a chariot pulled by cats, and Thor, a chariot pulled by goats.
Odin was also known for giving away gifts, specifically, gifts that had been made by his magical elves, Thor's hammer being one of them, and these elves were known as Odin's men. Odin is also referred to as Jólfaõr, or Yule Father, for he is the one honored during the season of Yule with feasting, drinking, gift-giving to strengthen ties between people.
It seems ridiculous to compare our fat, chimney sliding Santa to a one-eyed Norse god of war, but remember that our red-suit, fur-trimmed fat man is only recent commercialization of Santa created by a popular Cola company who decided his colors should match theirs.
Odin would take different forms to suit his needs. One, in particular, was of a man with a long white beard and a broad-brimmed hat. He donned this attire when he traveled the nine worlds seeking knowledge. If we compare this to early versions of Santa, who either wore a hood or a broad-brimmed hat, we can see the similarities.
Santa on the left, and Odin on the right. (Picture on the right was created in 1886 by George von Rosen).
Well before 'Twas the Night Before Christmas in 1823 and Santa's massive makeover by the previously mentioned Cola company in the '20s and '30s, he was depicted as a tall, gaunt man with a long beard who rode a horse and distributed gifts among those who had been good.
Odin's "the Wild Hunt" could happen during any winter storm, but particularly during Yule. During this hunt, Odin would bestow gifts upon the good and punish the bad while chasing away the darkness and crushing ice giants. Children would leave straw and carrots in their boots for the hungry Sleipnir, and they, in turn, would receive gifts in their boots in exchange. This tradition is also a part of Saint Nicholas Day, in which people leave presents in each other's shoes.
In addition to creating the world and giving us life, Odin would often give special gifts to people to help them overcome their fantastic obstacles. In Volsunga Saga, Odin arrives in his old man disguise to give Sigmund the gift of a magic sword. In the Saga of Hrolf Kraki, King Hrolf refuses the hospitality, armor, and weapons from a one-eyed old man believing he was better off. It's only later he realizes that he denied gifts from Odin and dies as a result of not having Odin's weapons.
In the Eddic poem, Volupsa en skamma, Freya talks about Odin's gift giving.
"We'll ask Odin
to keep us in mind
he gives gold to those who are worthy.
He gave Hermoth a helmet and armor.
He gave Sigmund a sword as a gift.
He gives victory to some,
money to others,
eloquence to many,
and common sense to all.
He gives waves to the sea,
word-skill to poets,
he gives many the happiness of love"
Odin was also thought to be all-knowing, each morning he sent his two ravens, Huginn and Muninn, to collect news from the world and to report back to him each night. He also traveled widely in search of knowledge, and the Norse believed he would know whether they had been bad or good, so they were good, for goodness' sake.