Many modern Pagan and Druid traditions consider Samhain the holiday which marks the end of one year and the beginning of another, although what I've read by historical scholars indicates that this was likely not so for the Iron Age Celts.
I've been on an academic calendar most of my life -- first as a student, then as a university employee -- so it often has felt to me that a new year begins around the beginningof September.
Also, I feel that my year is divided into two seasons, summer and winter. Summer is when after work, it's warm and light, so I spend time outdoors, and when green leaves are all around me, while winter is when it is dark and cold when I get home from work, and the trees are bare.
It never made much sense to me to observe the new year on January 1, which it's not the beginning of anything, it's smack dab in the middle of winter.
Nor does Samhain feel like a new year. From the academic calendar perspective, it's smack dab in the middle of a semester. And while the falling of leaves indicates that an old year is dying, a new year is far from coming.
I think now as a druid observing the stations of the sun, it makes sense to observe winter solstice as the new year. That's the time when the sun has finished moving away from us, and begins to move toward us -- one year has finished dying, and another year begins to grow. From that perspective, January 1 isn't such a bad time to observe the new year after all. They talk about the 12 days of Christmas, so how about the 12 days of the new year, December 21-January 1.