Actually the saturnal dates where pushed back to the end of December especially to fuck with the christian date of 25, (under diocletian i think ?) pretty much to fuck with them
If I remember correctly the origin of this celebration was very old, and the purpose was to celebrate Saturn, that was a roman god and, after the hellenization, fused with the titan Cronos, father of Zeus, Ades and Poseidon. It was only during the Empire that the fest was put in late december, but I think it was Domitian and not Diocletian. I honestly don't know if his puropse was to fuck the christians or not, but I belive that, since they were still persecuted at the time of Domitian, romans didn't care about them so much. Perhaps you are right, I don't know, but I belive that, since the hellenic faith was well establishd in all the territories of the Empire, when christianity was accepted and proclamed official religion, most of the pagan traditions were absorbed into the new religion and, allow me to say, "converted" into christian's one. Like Saturnals. I think that the most proper translation from latin should be Saturnalia by the way, but I'm not 100% sure.