Over time, the months shifted on the calendar: September, October, November, and December -- so named because they originally were the seventh, eighth, ninth, and tenth months -- became months 9 through 12 and March was moved from the middle of the summer to earlier in the year to make room for July and August (named after Julius and Augustus Caesar).
The four-week furlough for non-essential military personnel became associated with the Roman god of war Ares (who became known as Mars going forward) because it was spun by Roman aristocrats as a tribute to the state's warriors and not just a cost-cutting measure to reduce Rome's ballooning military budget. In this regard, March Break can be seen as an antecedent to contemporary holidays like Veteran's Day, Memorial Day, and Remembrance Day. Folks were more into military glory back then so things got blown out into almost a full month.
St. Patrick's Day, however, has nothing to do with March. So stop making the month about drinking and the colour green.