The problem with this idea is that the dating had nothing to do with celebrating Christmas. It was simply theological musing to do with Easter.
It seems like it wasn't celebrated until many decades later.
Where's the problem? Given the other dates thrown about, as well as Biblical clues that suggest the Nativity occurring during times more likely for shepards to be out with flocks and censuses being taken, it seems like placing a special importance on the solstice played a part. St. Augustine alluded to this in a sermon:
"Hence it is that He was born on the day which is the shortest in our earthly reckoning and from which subsequent days begin to increase in length. He, therefore, who bent low and lifted us up chose the shortest day, yet the one whence light begins to increase."
Augustine's Sermon 192
If they had appeared a century or so later that might be plausible.
That these "pagan" traditions didn't appear until the best part of 1000 years down the line is certainly totes sus..
Didn't appear as in they weren't documented by Christian writers?
Likely they survived in folk traditions or in synchronizing traditional beliefs or customs with the new religion. This isn't uncommon; the African diaspora religions are a good example of how ancient beliefs can survive time and attempts to destroy them.
Were that the reason (which is unlikely), then it would indeed be Christian.
It is a folk legend concerning the Donar's Oak, attesting to the importance of tree worship in pre-Christian Europe. The argument for the conifer tree that I have heard (and I thought was connected to Martin Luther) was that the triangle shape of the tree relates to the Trinity.
Regardless, I haven't read much opposition to the point that bringing in evergreens and even decorating them predates Christianity, even if it wasn't a full tree.
Christianity changed massively and it was organised and supported by multiple major institutions and underpinned by a comprehensive written tradition.
"Paganisms" were dead religions without institutional support or written tradition.
That authentically "pagan" traditions survived 1500 years in folk memory alone then reappeared and blossomed is somewhat fantastical.
The Saxons weren't converted until the 7th to 8th century, and the Scandinavians were mostly pagan right into the 11th century. And, as I stated earlier, conversion, forced or otherwise does not mean loss of cultural elements. These often become a part of folklore.
I find it hard to see some 19th C yank writing a poem as the resurrection of an ancient pagan tradition. The Romantic and "Volkish" traditions may have struved towards reviving "pagan" traditions, but they were mostly contrived rather than authentic.
Clement-Moore was inspired by Irving's depiction, and both writers wrote partially based on romanticizing European culture, particularly Dutch.
And, what the Romantics were doing may have been contrived, but there wasn't much of a choice in the matter. That doesn't remove the inspiration to look beyond Christian tradition.
Giving gifts is just too generic to belong to any culture.
It's like saying when someone today lights a candle or gives some flowers because they like the aesthetics they are somehow engaging in pagan ritual.
We're talking in the context of gift-giving associated with winter festivals. Gift-giving certainly is an old custom, and how does being generic not relate it to something besides Christianity? My point is in showing how Christmas traditions need not be connected solely to Christianity.
Other than as a shorthand for diverse pre-Christian "religions" it's pretty meaningless.
Even if you look at specific paganisms it's hard to differentiate "religious" practices from general culture or behaviour. Even the concept of religious and secular is Christian.
It's a Christian term that makes little sense outside of a Christian worldview.
It used to be a Christian term, and specifically a Roman Christian term. But, as language has a habit of doing, we use the term today with various but related meanings. Luckily, dictionaries provide us with guidance:
Definition of PAGAN
It makes sense today, where Christianity is the dominant Western religion, to describe both non-abrahamic religions (historical and modern) and cultural and spiritual practices that are primitive, or "nature based" as "pagan."