You assessed correctly except for month of December attributed to Christians, or so we think.
The birth of Osiris coincided with the day of the summer and winter solstice, depending on the hemisphere, and on this day the sun god would ride through the heavens in his chariot. The sungod Helios would ride through the sky in his sun chariot drawn by horses as depicted in the great fountain of Versailles. In the Hindu culture, it is the Sûrya, and his horse-drawn sun chariot, driven by his charioteer Aruna who rides across the sky, and in other cultures the chariot is drawn by other animals such as the goat (Zeus) or the reindeer. This same pagan practice is held in high esteem to this day, and has virtually successfully supplanted Jesus Christ as the main feature of Christmas. On the 25th of December, Santa rides across the skies in his reindeer drawn chariot. He is made acceptable by his friendly rotund appearance as introduced by Walt Disney, but he has the same characteristics as the ancient sun deities.
Origin of Santa Claus: 4th century: Historical evidence shows that St. Nicholas never existed as a human. He was rather a Christianized version of various Pagan sea gods the Greek god Poseidon, the Roman god Neptune, and the Teutonic god Hold Nickar. In the early centuries of the Christian church, many Pagan gods and goddesses were humanized and converted to Christian saints. When the church created the persona of St. Nicholas, they adopted Poseidons title the Sailor. They picked up his last name from Nickar. Various temples of Poseidon became shrines of St. Nicholas.[xxiv]
The theology of Santa is also in line with this thinking, since Santa, as taught to most children, has the attributes of God.
1. He is virtually omnipresent. He can visit hundreds of millions of homes in one night.
2. He is omniscient. He monitors each child; he is all-seeing and all-knowing; he knows when they are bad and good. He can manufacture gifts for hundreds of millions of children, and deliver them in one night each to the correct child.
3. He is all-good and all-just. He judges which children have shown good behaviour and rewards them appropriately. Bad children are bypassed or receive a lump of coal.
4. He is eternal.
Want to know about Ishtar (Easter)also?.
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There is a lot of debate about which group of people the Nicolaitans really are/were. One could as easily argue this refers to Santa worshippers/believers. Funny coincidence, too, that Santa is a jumble of the same letters in "Satan".