0: There has never been an unified religion of “paganism”. It is an exonym Christians use for their out-group. Therefore, the underlying premise is fundamentally wrong.
1. A generic “winter-god”, no culture specified? Sounds legit.
The actual origin of the christmas tree is far more likely that mystery plays of the Garden of Eden would take place on Christmas Eve (the patron day of Adam and Eve), where evergreen trees would be devorated with apples (eventually becoming coloured glass spheres) to represent the Forbidden Fruit, of which people would take branches home. The Christmas Tree proper was invented by Martin Luther, centuries after the Christianisation of Germany.
2. “The star […] has nothing whatsoever to do with Christianity.” …wow. I think you need to reread Matthew 2.
Also, a symbol so basic that it would be surprising that it would be weird if it wouldn’t appear in many different cultures in different meanings.
5. …this is not worth a refutation.
6. “Santa” is derived from “sanctus/a/um”, meanning holy, as in its English cognate “saint”. It it the feminine form of the Saint title in many romanic languages, although in this case, it is actually from the Dutch form “Sinter”. Santa is a title, his name is “Claus”, a short version of Nicolaus, specificially 4th Century bishop Saint Nicholas of Myra, famous for the many stories of him sneaking in saving gifts for families in need.
7. Santa’s sled being drawn by reindeer first appeared in 1821. Notably, it only was one reindeer, with eight reindeer only being introduced two years later. So again, far too late for a “pagan” origin.
9. …the fact that, as I said, this treats “PAganism” as an actual religion rather than just Christianity’s outgroup may be the least stupid thing in this one…
12. No, Mess is specifically a Christian ritual. It is the Mess held to celebrate the birth of Christ. Simple as that.