If you read that report and watch forecasts on tv, the snow is going to be in the North (mainly Scotland/high ground of Northern England). I'd very much doubt if we'll get anything more than a few sleety/hail showers and a few frosts - IF the sky is clear overnight.
Maybe more likely for Wednesday/Thursday is two bright sunny days with a few showers and temperatures around 10c - much much better than today's mist/murk/drizzle!!
But all in all that's what Spring is all about - it's in between winter and summer so all weather types are likely at times

.