Here you go:
March colder than February (7 instances + 1 tie):
1883 (tied), 1887, 1890, 1891, 1909, 1932, 1960, 1984
March colder than January (11 instances):
1876, 1880, 1890, 1906, 1916, 1932, 1933, 1937, 1947, 1950, 1960
March colder than previous December (19 instances):
1885, 1890, 1892, 1896, 1906, 1912, 1914, 1924, 1932, 1940, 1941, 1947, 1950, 1957, 1960, 1972, 2013, 2014, 2015
Surprisingly, 2016 didn’t make the list here- even though December 2015 was the hottest December ever, March 2016 was also 6th hottest March.
March colder than all three (3 instances):
1890, 1932, 1960
A few things struck me as interesting- first, it's happened more times in January vs. February, despite February having a higher average temperature. Second, it wasn’t too unusual for March to be colder than January before 1960, then it suddenly stopped happening. Third, our recent December futility/torches are apparent here.