It all depends on what you believe, but majority of our beliefs originate from the old Germanic or Anglo-Saxon religions.
Yule logs, yule block, yule trees, and even yule singers all adapted into Christmas traditions.
You are correct about the yule log being a ceremonial log burnt in celebrating surviving the harse environment and being able to witness the rebirth of the world. The yule tree is also a place to hang memorials for lost souls, ie Christmas ornaments, and it is usually placed on a symbolic cloth tree skirt, that represents the sun and life giving power. Also wreaths are made from removed branches which also represents the sun
Origins and specific practices vary greatly in interpretation.