Nonsense. You're conflating tradition (tree in this case) with festivals and ancient religious rites. See:
- Yule
- Dísablót
- Koliada
- Lohri
- Saturnalia
- Yaldā Night
- Nardoqan
- Yule
- Dísablót
- Koliada
- Lohri
- Saturnalia
- Yaldā Night
- Nardoqan
In the absence of evidence about the timing being affected by other festivals and in the presence of much evidence that all the actual traditions are far more recent than pagan, I don't believe it's fair to claim Christmas has pagan origins. The absolute best we can do is say that its timing may have been influenced by other, pre-Christian celebrations.
Here's another one on Saturnalia from the same scholar:
Later during Soviet times secularish Christmas traditions including Ded Moroz were moved to New Year's.