This ends up being one of the biggest complaints from a lot of Pagans, especially newbie Pagans; why don't we have any solstice music? Well, we do. In fact a lot of the music that we consider traditional for this time of year, while the word "Christmas" may be part of it, is very Pagan in nature. ("O Tannenbaum", anyone?) It's just in how you look at it and how overly sensitive you might find yourself to references to the Christian holiday.
As an aside, and I mention this just about every year during the 21 Days of Yule because someone always ends up asking why there's no Lorenna McKennitt in the Yule playlists I post. For the most part her holiday music is more traditional Christian/Christmas music. While Lorenna McKennitt is a favorite among Pagans because of her Celtic and world music sounds, she herself is not Pagan and her holiday music tends to be more traditional. I typically don't include any of her music in my holiday list for that reason. Believe me, I love her music and have nothing against her!