The far north of Scotland would be affected by snow showers all day, he added.
Scattered rain, sleet and snow showers will continue on Monday morning, mainly across east and southeast.
The Met Office said sleet and snow showers would become more widespread on Friday afternoon.
Snow showers are to gradually ease on Saturday afternoon and become much more isolated.
The Met Office said Friday's snow showers would continue into Saturday, with most of it falling on hills.
Light snow showers are possible in the county later, the Met Office said.
Further sleet or snow showers are expected later on Tuesday, but they will turn to rain as the afternoon approaches.
The Met Office said following sleet and snow showers, widespread icy roads were likely to form on Tuesday evening and overnight.
Widespread ice on untreated roads and "very poor visibility" during heavy snow showers would make driving conditions dangerous, the Met Office warned.
Further snow showers, heavy at times, have been forecast for County Durham, Northumberland and Tyneside, with the Met Office issuing a yellow alert.
Heavy snow showers have already swept across parts of eastern England and Scotland, forcing the cancellation of Middlesbrough's premiership clash against Fulham on Teeside.
Temperatures in parts of the UK plunged to -11C (12F) overnight as forecasters warned of a bitterly cold spell and snow showers over the weekend.
Next week would generally see drier and brighter conditions, but it was expected to remain very cold and some snow showers were likely, the forecast said.
Up to 5cm (2ins) of snow was forecast for eastern England during Thursday, with snow showers possible in Aberdeenshire, the Midlands, the South East, Pembrokeshire and Cornwall.
Heavy snow showers made conditions more difficult for the favored later starters and Norwegian legend Ole Einar Bjoerndalen failed in his bid for a 10th Olympic medal.
Forecasters have said there could be more snow showers later.
Looking ahead, he said wind and snow showers were "likely to continue across north-eastern and central parts of the country, although the odd wintry flurry is possible almost anywhere".
According to the National Weather Service, scattered snow showers in Vail -- home to one of the nation's best-known ski areas -- were expected to linger into Monday evening.
Snow showers already swirled around a few hundred spectators.
Up to 5cm (2in) may fall in the central belt and as much as 15cm (6in) could gather on higher ground, with only the far western coast likely to escape snow showers.
The Met Office warned that heavy snow showers were expected across much of Scotland, Northern Ireland, and parts of north-east England, with up to 20cm of fresh snow possible in places by the end of Sunday.
The band of snow will be followed by some showers which may fall as snow on higher ground, he added.
But he is approaching a winter storm that includes rain, showers, thunderstorms, thunderheads, snow and possible icing that makes changing course not only desirable, but advisable.
"With Minnesota, ain't no telling when the snow's gonna come, you know, " said Showers.
Showers continued through much of the day, falling as snow in the Scottish mountains above around 200 to 300 metres and over the peaks of the Pennines and Welsh mountains.
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