This is a good question and I would like to add my two cents, as a parent.
When you have children, this particular "holiday" gets crammed down their throats everywhere they go...to include school. The traditions of others *does* affect other people or there wouldn't be an issue. IOW, I wouldn't care at all about what people believe in, if they didn't try to instill those beliefs on my child without my consent.
We deal with this every year, and every single year someone asks my son what santa brought him for Christmas. And every single year my son responds with "Santa isn't real."
Amazingly, people get truly offended by his honest response, especially if their own children are somewhere within ear shot. So my motto...don't lie to my child about santa, and he won't tell yours the truth.
They can do all kinds of santa related activities at school, but they don't tell children about Jesus, it's illegal, right? So even though I hear it every year, that Jesus is the reason for the season, anyone with eyes and ears knows that simply is not true.
I didn't read through this whole thread, so I don't know if anyone answered with these verses as to the time of Christ's true birth, but here are some simple scriptures regarding that:
Luke 1:36 tells us that Mary became pregnant 6 months after Elizabeth. Luke 1:56 tells us Mary stayed with Elizabeth for 3 more months - putting Elizabeth to a full 9 months. But we find that Mary left her at this time. Why? Luke 2:41 tells us it was to attend Passover. When is Passover? SPRING. Which puts Christ's birth 6 months later. Late Sept or Oct.
Peace out.