CapriUni's new Solstice carol, "Raise All Your Voice" is a good one for the Roman calendar new year's, too.

I don't have the link handy, but type "solstice" in the filter and search the last 90 days and you'll find it.

Also, IIRC, Jeri posted a new New Year's song last December and the thread was refreshed recently.

Genie

It's also a good time for "circle" songs, like "The Circle Game" [Mitchell], "Circle" [Chapin], "Turn, Turn, Turn" [Seeger] and reminiscing songs like "In My Life" [Lennon-McCartney].