I don't think it worked. God said specifically:
Deu 12:29 "When the LORD your God cuts off from before you the nations which you go to dispossess, and you displace them and dwell in their land,
Deu 12:30 take heed to yourself that you are not ensnared to follow them, after they are destroyed from before you, and that you do not inquire after their gods, saying, 'How did these nations serve their gods? I also will do likewise.'
Deu 12:31 You shall not worship the LORD your God in that way; for every abomination to the LORD which He hates they have done to their gods; for they burn even their sons and daughters in the fire to their gods.
Deu 12:32 "Whatever I command you, be careful to observe it; you shall not add to it nor take away from it.
And so what have we done? Taken every pagan custom, myth and observation of non-Christian societies and polluted our worship of the Lord...exactly what he said not to do.
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...