Actually what they were really aiming at was the cult of Mithras which was the Church’s biggest rival in the Roman empire, and was very popular with the lay military. The old classic gods usually associated with Rome and Greece had long fallen out of favor despite what Shakespeare would have you believe.
Mithras’ big day was December 25th in the old Roman calendar. Others say that it was The festival of Natalis Invicti , the holy day devoted to the Sun, also held on that day.
The Christmas Tree part was what was lifted from the Celtic pagans.