The models currently seem to be hinting at more significant snowfall
over the weekend and early the following week, associated with a low
coming down from the north. Could be a messy picture as milder air
gets dragged into the south, but many of the classic snowfalls of the
1980s were "marginal" events with moist warm stuff adding to the mix.

This coming week I would say eastern parts could well get some snow
any time from Tue/Wed onwards, with the chance increasing the further
you go through the week.

All very much subject to change of course!