The tree is a substitute sacrifice. Burning the Yule Log at the end of the season is nothing more than the burning of the substitute sacrifice.
If there's a single religious element left in the public presentations this time of year, it's that X-mas tree!
(Note: The "X" is from the "Icthus" - "Fish" symbol of the early Christians. "X" is a valid representation of "Christ" within Christian history - it is not some pagan or secular substitute.)
(NOTE: today I learned about when "the Lord", or "Vishnu", or the devine person identified as "God", as distinct from Brahmin, aka "the Universe", manifested Himself in the days of the prophet Noah - known as Manu in Hindu holy scripture - He did so as a "fish". Manu - or Nu - or Noah - tied his boat with his 7 personages on board to a large "fish" and was thereby saved.)
(NOTE: the Hebrew story of Noah requires God to deliver the word directly to Noah because, after all, Judaism does not admit of the three-person nature of God. As a result Noah had to build his own boat. In the Hindu version the religious point of view is much more like that of Christianity so God can simply send His own fleshly manifestation directly to Noah to save him. Tradition holds it that God did so in the body of a large fish. - Uhh, see Jonah and maybe Jeremiah's Juggernaut - I would imagine the Moslems went absolutely nuts when they first encountered Hinduism!)
(NOTE: Uh, the Moslems claim Nu - or Noah - as "one of their own".)
(NOTE: Hindus claim Krishna, God's "in person" fleshly manifestation, may be symbolized by a large snake - usually a King Cobra. Moses ALSO used a snake on a pole as the symbol of his socio-political movement, if not of God Himself.
Now, after wading through all of that, it is also worth noting that the X-Mass tree tradition predates Rome. It's really old.