No, they did not. They started out as pagan, and got assimilated by Christianity, which spread them around. Even the date 25 December was picked because it coincided with the Saturnalia celebrations. And the date of Easter differs between the eastern and western orthodoxy (Eastern Orthodox Christians celebrate Easter on the Monday after the last day of Passover; Catholics and Protestants — and thus Western Europe and the Americas — celebrate Easter on a Sunday calculated by a wholly different timetable.