What you say is correct...Way back when, Constantine brought religion and paganism together so he could rule over both factions without constant fighting...And with the power and might of Rome, there wasn't much that was going to change that rule and practice over the Centuries...
Jesus was not born during the Winter Solstice and we are never encouraged to celebrate the birth of Jesus...It's unfortunate I suppose that somewhere after the fall of Rome's power that some large church did not decide to have a holiday for the celebration of the birth of Jesus sometime in the fall without the trees and festivities and other pagan junk...
The consolation we can have is that while Jesus is likely shaking his head as he watches us we are conforted knowing we are not under the law but under grace...
During the Judgment Seat of Christ the record of these activities we do will be burned and not be part of our record presented before God...