There are generally two different ideas as to why Christianity associated Jesus' birth with the winter solstice:
I was taught in my world history class that Christians got much of their symbolism and holidays (Lent, for instance) from the Romans; the Roman emperors, especially Nero, were extremely cruel and genocidal towards the Christians. Those who did not celebrate Roman festivals were under suspicion of being Christian, and so these people were targeted. So, the Christians began celebrating Roman holidays under the plot of worshiping Y'shua ha'Machiash. Christmas was the
Saturnalia to the Romans. A second reason is that the Catholic Church, during much of the Middle Ages and beyond, were conquering Pagan areas. This may be where they got the ideas such as gift-giving and the use of the pine tree as incentives for Pagans to convert to Christianity. These two concepts specifically were from the celebration of
Yule, a Germanic holiday.
As for Santa Claus, he comes from the Greek Bishop of Myra
Saint Nikolaos the Wonderworker, or Saint Nicholas. He had a reputation as a gift-giver, providing coin to beggars and friends by hiding them in their shoes as they slept, which is where the French get their celebration of putting gifts in children's shoes instead of in stockings, as is traditional in America. The look of Santa Claus was largely influenced by
Thomas Nast and
Clement Clarke Moore's "A Visit from St. Nicholas".
Jesus' birthday was likely in Spring.
Luke 2:8 (NIV) says, "And there were shepherds living out in the fields nearby, keeping watch over their flocks at night." Shepherds do not flock their sheep during the nights of Winter. They usually do this during the Spring.
I hope that helped answer your question.
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