The December 25 date doesn't come from Saturnalia. Saturnalia celebrations were from the 17th to 23rd. It seems to have developed side-by-side with Sol Invictus. Whether the latter directly influenced the former, nobody's sure - there is a lot of conflicting evidence.
There are two main theories that attempt to account for how, where and when Christmas became incorporated into Christian liturgy - the History of Religions Theory (which JWs take some of their ideas from) and the Calculation Theory. According to the Calculation Theory, December 25 derives from the Annunciation (Conception) of Mary which, for various reasons to do with symbolisms, e.g. Spring, Creation of the world, prophets dying on the same day as they were originally conceived/born, some early Christian groups believed this happened in March, e.g. March 25. Count 9 months and you get December 25.