For the record (because this gets to me), it wasn't a winter solstice festival, which is why it isn't on the solstice! In Jewish thinking of the time, prophets were thought to typically die either on the day they were born or the day of their conception. The day of Jesus's death was (more or less) known; there were Very Serious Arguments about whether to celebrate his birth on the same day or not. "Or not" won, so we celebrate his birth nine months before Easter. "Or not" won to such an extreme degree, in fact, that in the Latin-rite Catholic Church if the feast of the Annunciation would coincide with Easter, the feast of the Annunciation gets moved to avoid that. (In the Eastern rites and in the Eastern Orthodox Churches, it doesn't get moved, and the prayers just get changed a bit.)