They don't just happen to coincide, the mid-winter solstice celebration was "Christianized", choosing December 25 as the birth of Christ. No such date is found anywhere in scripture. In fact, it was more likely he was born around the time of harvest in the Fall, as that is when they would call for a census to determine taxation. December 25, is purportedly the birthday of the god Tammuz. That's what I've read, but can't attest to its veracity. It certainly is not something from scripture or early Christianity either, for that matter.To me Christmas is two separate things:
1) A celebration of the birth of Jesus Christ
2) A winter celebration/feast
They just so happen to coincide, regarding time and date - and share the same name!
But to me they are separate
One is Pagan in origin, the other Christian
But none of that actually matters. It's what people choose to see it as, and celebrate it as such. I sincerely doubt God cares if it's historically correct. Only legalist thinkers think it matters to God. Romans 14: 5-6
One person considers one day more sacred than another; another considers every day alike. Each of them should be fully convinced in their own mind. Whoever regards one day as special does so to the Lord.