The Christmas Tree isn't of "pagan origin." In fact, of all things related to Christmas, it's probably the only one that is almost entirely a product of a Christian culture.
Not that it really matters; the insistence that "Christian" practices be pure and untainted by non-Christian (i.e., "pagan") practices is a silly one that dates back (again!) to the Puritans (see below). Why we insist on keeping it up is another cultural practice very peculiar to Americans (equally peculiar is the idea that we are the world and our Christianity is world Christianity. But that's another hobby horse....).
The tree is a seasonal decorative item. Rather like the concept of communion, it springs not from some cultural icon co-opted by the new dominance of Christianity in the dark places of ancient history, but from Christian sources: specifically, the Genesis story and the Paradeisbaum inspired by German morality plays and the veneration of Adam and Even in the Eastern church which spread, unofficially, westward.
CHRISTMAS Eve is the feast day of our first parents, Adam and Eve. They are commemorated as saints in the calendars of the Eastern churches (Greeks, Syrians, Copts). Under the influence of this Oriental practice, their veneration spread also to the West and became very popular toward the end of the first millennium of the Christian era. The Latin church has never officially introduced their feast, though it did not prohibit their popular veneration. In many old churches of Europe their statues may still be seen among the images of the saints. Boys and girls who bore the names of Adam and Eve (quite popular in past centuries) celebrated their "Name Day" with great rejoicing. In Germany the custom began in the sixteenth century of putting up a "paradise tree" in the homes to honor the first parents. This was a fir tree laden with apples, and from it developed the modern Christmas tree.
That first connection, to traditional stage decorations, is not to be overlooked. The tree really is just a seasonal decorative item, just as Christmas in America is now just a time of year, with almost no connection to either Christ or the Roman Mass.
As Penne Restad documents it in Christmas in America, the small tree put up in German households on Christmas Eve (feast day of Adam and Eve) became the dominant feature of room-filling tableaus in 19th century America, tableaus complete with landscapes made of dirt hauled in for the purpose (think of Richard Dreyfus in "Close Encounters" hauling in dirt to build the Devil's Tower in his living room. Now cover it with snow....). It was never more than an excuse for decoration, in other words.
There's also the fact that, at best, you are only likely to see "Chrismon" trees in Christian churches, and then only in the worship space of some Protestant churches. You may find a decorated tree in a Christian place of worship, but odds are the decorations are specifically religious symbols, and even then the tree may (or may not) be up near the altar or pulpit. It's a secular decorative item, not a religious "Xmas" item at all.
So the tree we get so manic about now is as American as Santa Claus and 24 shopping days 'til Christmas.
And while we're on the subject, no, Christmas is not Saturnalia sanctified. It probably is taken from the Natali Invictii of Rome (at least when it started in Rome). But it also started elsewhere on January 6, and where it was set on December 25th the reasoning had to do with the Day of Atonement and Zechariah's Temple duty. You could look it up. The idea that it was the Saturnalia is most likely from Increase Mather (or some other Puritan), who was no fan of Christmas to begin with, for reasons a lot of atheists and others sick of the holiday taking over the last 3 months of the American calendar might well sympathize with:
In the Apostolical times the Feast of the Nativity was not observed....It can never be proved that Christ was born on December 25....The New Testament allows of no stated Holy-Day but the Lords-day...It was in compliance with the Pagan saturnalia that Christmas Holy-dayes were first invented. The manner of Christmas-keeping, as generally observed, is highly dishonorable to the name of Christ." (quoted in Penne Restad, Christmas in America, New York: Oxford University Press, 1995, p. 14)You want a war on Christmas? Take it up with the Puritans. Although that last sentence could have been uttered today, rather than 300+ years ago; if you still want to protect Christmas from commerce. If you do, let me recommend Bill McKibben as your guide.
As for the word itself, that didn't come into use until 1038; at least, New Advent says that's the earliest recorded appearance of the word. The feast first appeared in 354 in Rome; as early as 200 C.E. in Alexandria. And as for "Xmas," well....we've done that.