Tradition tells us that during the pontificate of Pope Liberius, in the Fourth Century, in the heat of August, the plan of the church of St. Mary Major was traced out in a miraculous fall of snow. For this reason that basilica is known as St. Mary of the Snow, and the name is also given to the feast of its dedication. The stations at Christmas are held in this Church because some relics of the Crib of Bethlehem are preserved there. The Pope was also accustomed to officiate there on the first Sunday of Advent, at the beginning of the ecclesiastical year.
(Source: The New Roman Missal, Rev. F. X. Lasance)