Actually, it was never called Mass at Midnight in the missal. It always said Missa ad noctem, which is Mass at Night. Custom caused midnight to be used, because it was the first moment of the new day, but the missal never actually said this. It could have been done later in the night, at 1AM, 2AM, etc.
Anticipated Masses on the evening before, as we have today for Sundays and certain solemnities, did not exist until around 1970, so no thought ever would have been given to having the Christmas Mass at Night before midnight.Vigil Masses were an entirely different type of Mass, as they were penitential and always celebrated with no Gloria or Alleluia, always with the priest’s wearing violet vestments, and were celebrated the morning of the day before.