The City operates with a calendar of four months of 75 days: Dawn, Flame, Dusk and Sword. These months do not really correlate to any particular season, given that The City can border regions with different seasons, and maintains its own fairly stable climate through the Arcane Matrix.
By general consensus, regardless what month it was, it becomes Sword 1 when the Nightmare arrives. In addition, Arrival Day in a new world happens on Dawn 1, skipping any days that may have been left over in the rest of the year in the old world.