No, the Yule tree and Yule log are two different traditions. As the solstice approached, and the days gradually became shorter; many feared that the sun would eventually disappear forever, and everyone would freeze. But, even though deciduous trees, bushes, and crops died or hibernated for the winter, the evergreen trees remained green. They seemed to have magical powers that enabled them to withstand the rigors of winter.
So, ancient Germanic people tied fruit and attached candles to evergreen tree branches, in honor of their god Woden. The trees were viewed as symbolizing eternal life. The trees joined holly, mistletoe, the wassail bowl and the Yule log as symbols of the season. Ancient Pagan Romans decorated their trees with bits of metal and replicas of their god, Bacchus. They also placed 12 candles on the tree in honor of their sun god. All predated Christianity.
I was talking about the Yule tree. I've had this information shoved down my throat since I was young and I've dealt with enough de to know what I'm talking on.