The Jewish Calendar

"Christmastide" is traditionally the period from Christmas to New Year's Day and the term "Happy Holidays" was meant to cover this period. If said very early in the season it could be interpreted to include Thanksgiving, but generally this isn't the usage. Thus Christmas and New Years together have always been the big holiday combination, but with the gifts and decorations and music, it goes without saying that Christmas is the dominant of the two.
Unlike Christmas, Hanukkah is not the big holiday that, along with the New Year's celebration, brings the old year to a dazzling close. There is proximity between Hanukkah and Christmas but they are from different calendars. The Jewish calendar is different, with the Jewish year ending in the fall after their High Holy Days and with a different New Year, Rosh Hashanah, not on January 1st.
Hanukkah is overshadowed theologically by the High Holy Days, Passover, and other observances. As religious calendars go the Jewish cycle is extremely rich, with nearly a dozen special observances and celebrations, all with their respective meals and ceremonies. Hanukkah is a minor event in the Jewish cycle.
It is not mentioned in the Bible or Torah. By comparison the Christian calendar of holidays yields only two major holidays, and in North America, as in many other parts of the world, Christmas is the most important. Christmas is the preeminent holiday in the western world. Hanukkah is minor. This isn't a declaration of religious or any other kind of superiority. The fact is, Jews have a bigger holiday calendar, just not a big holiday in December.
The important Jewish holidays come in the fall. One autumn tradition in particular, building a sukkah on the holiday, Sukkot (The Feast of Tabernacles) stands out as one that must be at least as fun for children as decorating a Christmas tree. A hut is constructed in one's yard using branches, leaves and fruit, but without nails. It commemorates a time when the children of Israel were wandering through the desert, living in temporary shelters. It seems similar to the forts and clubhouses of my childhood. Participants get to eat meals inside the structure and to shake a palm leaf while reciting prayers. The smell of drying leaves in the early autumn weather and the creativity of inventing the hut must be as magical as the aroma and decorating activities associated with Christmas trees.