While it may be mostly Pagans who celebrate the Yule holiday today, nearly all cultures and faiths have held some sort of winter solstice celebration or festival. Because of the theme of endless birth, life, death, and rebirth, the time of the solstice is often associated with deity and other legendary figures. No matter which path you follow, chances are good that one of your gods or goddesses has a winter solstice connection.
Alcyone (Greek)
Alcyone is the Kingfisher goddess. She nests every winter for two weeks, and while she does, the wild seas become calm and peaceful. Alcyone was one of the seven sisters of the Pleiades.
Ameratasu (Japan)
In feudal Japan, worshipers celebrated the return of Ameratasu, the sun goddess, who slept in a cold, remote cave. When the other gods woke her with a loud celebration, she looked out of the cave and saw an image of herself in a mirror. The other gods convinced her to emerge from her seclusion and return sunlight to the universe. According to Mark Cartwright at Ancient History Encyclopedia,
"[S]he blocked herself in a cave following an argument with Susanoo when he surprised the goddess with a monstrous flayed horse when she was quietly weaving in her palace with her younger sister Waka-hiru-me. As a consequence of Amaterasu’s disappearance the world was cast in total darkness and evil spirits ran riot over the earth. The gods tried all manner of ways to persuade the peeved goddess to leave the cave. On the advice of Omohi-Kane, cocks were set outside the cave in the hope their crows would make the goddess think that dawn had come."
Baldur (Norse)
Baldur is associated with the legend of the mistletoe. His mother, Frigga, honored Baldur and asked all of nature to promise not to harm him. Unfortunately, in her haste, Frigga overlooked the mistletoe plant, so Loki - the resident trickster - took advantage of the opportunity and fooled Baldur's blind twin, Hodr, into killing him with a spear made of mistletoe. Baldur was later restored to life.
Bona Dea (Roman)
This fertility goddess was worshiped in a secret temple on the Aventine hill in Rome, and only women were permitted to attend her rites. Her annual festival was held early in December. High-ranking women would gather at the house of Rome's most prominent magistrates, the Pontifex Maximus. While there, the magistrate's wife led secret rituals at which men were forbidden. It was even prohibited to discuss men or anything masculine at the ritual.
Cailleach Bheur (Celtic)
In Scotland, she is also called Beira, the Queen of Winter. She is the hag aspect of the Triple Goddess, and rules the dark days between Samhain and Beltaine. She appears in the late fall, as the earth is dying, and is known as a bringer of storms. She is typically portrayed as a one-eyed old woman with bad teeth and matted hair. Mythologist Joseph Campbell says that in Scotland, she is known as Cailleach Bheur, while along the Irish coast she appears as Cailleach Beare. Continue reading from Learn Religions
Winter Weather Folklore (Farmer's Almanac)
Snow Queens and Winter Witches from Around the World (Folklore Thursday)
10 Evil Winter-Dwelling Beasts From Folklore (Listverse)
The Magical History of Yule, The Pagan Winter Solstice Celebration (Huff Post)
An Cailleach - The Irish Goddess of the Winter and Following Her Trail in Ireland (Irish Central)
Winter Tales and Myths: Where Did Old Man Winter, Jack Frost Come From? (AccuWeather)
15 Great Snow Gods You Can Worship For More Snow (Endless Rush Outdoors)