I can't believe this was even a question. There is no such thing as a Hanukkah tree. Or a Kwanzaa tree. Or a Festivus tree. If you're gonna have a tree on display during the month of December, and you plan to decorate it with Christmas lights, and Christmas ornaments, then, let's all be honest now, it is a Christmas tree.
People seriously need to get over their hangups, and let it be.
We're not forcing you to celebrate Christmas (although I personally know several non-Christians who enjoy the commercialized aspects of Christmas), so don't ask us to not celebrate.