score:2
It is probably somewhat, but not entirely coincidental.
We aren't 100% sure exactly why Christmas is celebrated when it is. The leading theory is that the date of Christmas was set to match (or rather, co-opt) a pagan Winter Solstice festival. The specific festival most point to was Sol Invictus. Historians going as far back as the 12th century were reporting this theory. Sol Invictus being the Roman sun god, the timing of his festival just after the Winter Solstice (the day with the least sunlight all year), is no coincidence.
Another prominent theory is that it is tied to the date of the Vernal Equinox (exactly 9 months later to be precise), which of course indirectly also ends up placing it just after the Winter Solstice.
So while the date was set before the Germanics were converted, the fact that it coincides with (and perhaps helps co-opt) their own "Yule" solstice festival, isn't exactly a coincidence.
Upvote:0
You may want to read the following related question: Were there Gifts on the Days Leading Up to Christmas?
To paraphrase what it says there:
In Scotland, the twelve days of the Yule festival, called Da latha dheug na Nollaig, were celebrated according to the traditions of the viking invaders and they had the custom of giving gifts on all twelve days from Christmas Day to the Day of the Epiphany. You can find a long rundown of these and similar customs in Keary's book "Outline of Primitive Beliefs" (1882). The Golden Bough by James Frazer also has a long article on it.