Other than 2013 and 2018, March really isn’t that great for snow. Unlike the winter months, it seems to be either all or nothing. All if we strike lucky and get unusual Synoptics and nothing if the month is anticyclonic or the standard Atlantic-dominated.
Looking back through the 90s and 00s, most March snowfalls tended to be transient affairs within a more mobile pattern. The more high pressure dominated Marches then largely avoided snow altogether.
I still think any snow this winter is going to come from northwesterlies or northerlies as high pressure slides west or southwest. Any favourable Synoptics will likely appear from April onwards which will either just deliver cold rain or even warm settled conditions.