A band of heavy snow could cause disruption later this week, with as much as 20cm possible in higher areas.
Temperatures will drop as the week goes on, with a yellow snow warning issued for Thursday and Friday.
Most of Scotland will escape the worst of the weather, with the alert centred on Wales as well as northern and central England, the Met Office said.
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However, before that forecasters have warned people travelling could face difficult driving conditions and transport disruption with ice alerts issued for parts of the country.
The Met Office has issued a yellow snow and ice warning for the Highlands, Western Isles, Orkney and parts of Argyll and Bute and central Scotland which runs from 3pm on Tuesday until midday on Wednesday.
It warns that accumulations of 1-3cm of snow are likely quite widely across the warning area, with perhaps another 5-8cm over the northwest Highlands, while icy surfaces will be an additional hazard.
A separate yellow warning of snow in Shetland is in force until 3pm on Tuesday
The later warning runs from 3am on Thursday to 3am on Friday and stretches from the Scottish Borders down to Cambridgeshire and the Midlands in England.
One to two centimetres is widely possible at low levels, 2-5cm on ground above 200m, and as much as 10-20cm above 400m.
There is a risk of power cuts, travel delays and some rural communities becoming cut off, the forecaster said.
The snow will ease later in the day, and may turn back to rain or drizzle, especially in the south and east.
There is uncertainty with respect to the rain-snow boundary, and the northern limit of the snow, the Met Office said.
Met Office deputy chief meteorologist Chris Almond said: “While the early part of this week will see some rain, at times heavy, gradually sinking southwards, there’s an increased signal for wintry hazards as we move through the week as cold air from the north moves over the UK.
“It’s from Thursday that the snow risk becomes more potentially impactful, as mild air attempts to move back in from the south, bumping into the cold air and increasing the chance of snow developing on the leading edge.
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“While there are still lots of details to work out, the initial snow risk looks highest in northern England and Wales from Thursday.”
The snow will turn into sleet and rain towards the end of the warning period from the south.
Further warnings for ice could also be issued later in the week as temperatures drop below average for this time of year, the forecaster said.
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