There's no empirical evidence March is cooling (or warming less fast) than the other winter months. In fact, November has been one of the colder months in the last decade during the cold season. January had no warming trend here for like 5-6 decades, so we're probably regressing to the mean a bit....aka, we were "due" for a stretch of putrid/warm Januarys.
Tip and I have sometimes discussed that maybe there is a response on the extreme end of the spectrum for individual cold intrusions....more frequent snows in October and late April/early May than we've seen in the past, but they manifest themselves within the warmer climate background signal.