Wouldn't lose any sleep over this timid threat of snow now, it's starting to fall in line with the weather the country has had prior to this cooler spell.
Best to wait until at least the 3 day timeframe comes in to play, runs will continue to bounce N/S/E/W. Even within 24 hrs it is difficult forecasting weather around the UK.
Temp hovering just below 2C, maybe if this has a daytime temp, a bit of sleet/wet snow may of been in the mix, but it's not, so looking forward to another 18/24hrs of cold rain.
Misty and murky out, looking like some rain on the way shortly, temps still slowly creeping up, have been since yesterday evening, so not too surprised at the thawing, up to 1.5C now.