It all depends and it is complicated. Christmas is December 25 because it is 9 months before March 25 (The Annunciation) for Reasons. It was also when the Spring Equinox was in the 4th century when dates were established (The first Sunday after the first full moon after the Equinox).
If you move the current Calendar so that Jan 1 in the first week after the equinox, of course all annual events will get messed with. If you create a new Calendar (Ala the French Revolutionary Calendar), Christmas will still be observed ~five days after solstice. Regardless of whether you are Old or New calendar.
Oh Rat, if they leave it up to you, just give them the easiest thing to make.Yeah, I know, that’s not as funny, but …