Well, the trees were originally a pagan symbol.
But that symbolism ended when Europe was Christianized by about 1000 A.D.
I don't think the tree in Christmas re-appeared until some time well after that date. But by then it had assumed its use as a "Christmas" Tree and was generally recognized as such until relatively recently.
Its true that many non-Christians celebrate Christmas in a secular way and they may also put up a tree, but referring to it as a "Holiday" tree when the majority of people use it as a Christmas tree appears to be stretching political correctness.