The year in the Roman calendar naturally starts on March 1. After all, the words September, October, November, and December literally mean Seventh Month, Eighth Month, Ninth Month, and Tenth Month, respectively.
Keeping track of the passage of years was primarily the concern of those keeping historical records. Ordinary people were not particularly concerned with long-scale time reckoning. In many ancient cultures historical events were dated in regnal years, i.e., using a time reckoning system starting with the anniversary of a sovereign’s accession or coronation. Under this system, the first day of the new year is the anniversary of the king’s or pope’s accession, i.e., the new year’s day would change with every new ruler.
In most cultures, new year’s day was not a cause for celebration for its own sake. People may have celebrated the anniversary of the king’s ascension or some religious feast, and the fact that these were used in time reckoning as dividing points between two consecutive years was quite secondary. In medieval Europe, March 25 (the Annunciation) was probably the most widespread new year’s day but the practice was far from universal. For instance, Rome used December 25 while Florence used March 25.
January 1 became new year’s day gradually from the 14th to the beginning of the 19th century.