I am actually surprised Birmingham hasn't done better for snow over the past few years considering 90% of the city is ideally placed between 100-200m above sea level, infact I think the Dudley area is about 200-250m.
I would of thought the city would do well from an Easterly, more especially a North Easterly with slightly less land for the convective showers to travel plus no high ground to block any degradation, also as already posted from a front approaching from the SW bumping into cold air in place.