Because the civil year begins in January, the month carries an unusual density of renewal rites. In Japan, Shogatsu brings millions to Shinto shrines and Buddhist temples in the year's first days for hatsumode, the first shrine visit, with the old year's amulets returned for burning and new ones taken home. Many Protestant churches keep Watch Night on the evening of the thirty first of December, crossing into January in prayer, a practice with deep roots in Methodist and African American congregations.
For Western Christians the sixth of January is the Epiphany, closing the twelve days of Christmas with the visit of the Magi, while Eastern churches keep the same date as Theophany, the baptism of Christ in the Jordan, marked by the great blessing of waters. In Ethiopia the related feast of Timkat follows on the nineteenth of January, when replicas of the Ark are carried in procession to the water. Churches that follow the Julian reckoning celebrate Christmas itself on the seventh of January, a reminder that the month's dates depend on which calendar is doing the counting.
Beyond Christianity, Makar Sankranti on the fourteenth of January is one of the few Hindu festivals fixed by the solar rather than the lunar calendar, marking the sun's entry into Capricorn with river bathing and kite flying, and the Tamil harvest festival of Pongal begins the same day. What January keeps, across all of these, is the older instinct that a threshold in time should be crossed deliberately, with attention to what is being left behind and what is being begun.
Sources Encyclopedia of Shinto (Shinto Jiten)Kokugakuin University with The Oxford Dictionary of the Christian Church, 3rd revised editionF. L. Cross and E. A. Livingstone (eds.), Hindus: Their Religious Beliefs and PracticesJulius Lipner