For Dreams Come True, this was their 5th No. 1, penned by vocal Miwa Yoshida（吉田美和） and composed by both Yoshida and leader Masato Nakamura（中村正人）. Even though the single was released just a week into the New Year, I think the slow jingle bells in the background can have people thinking that it was originally meant for the Yuletide. Plus, it is a romantic ballad, and in Japan, Xmas is all about the couples. "Winter Song" ultimately became the 19th-ranked song for 1994.
This is the concert version by Dreams Come True. (Ahh...no, it isn't. It's been taken down so enjoy this remix.)