I'm all for phrases like Happy Holidays, because there are people other faiths who are celebrating things at that time of year other than Christmas. I want everyone to be happy, so if I don't know which one you may be celebrating, I am likely to say Happy Holidays.
But I'm not crazy about a Christmas tree being anything other than a Christmas tree. That's what it has always been called, and I see no reason to change it now. AFAIK, decorating a tree isn't a tradition of any of the other Wintertime celebrations, only Christmas, so it should be called a Christmas tree. And don't give me a lecture about the pagan origins of the tree, because I'm not talking about Christian Christmas, but normal capitalist American secular Christmas.
Also, my daughter's school had a Fall celebration on October 31st instead of a Halloween party, and I dunno WTF that was about.