The Met Office has issued yellow weather warnings for snow in parts of the country, with the most severe snow in the more hilly parts.
A Met Office spokesman said: “As an area of rain moves northwards, it looks like turning to snow over parts of northern England, and then southern and central Scotland.
“Accumulations of 2-4 cm of snow are possible above 200 metres and 5-10 cm above 300 metres.
“Coupled with strong winds, gusting to 35 to 45 mph in places, this is likely to lead to some difficult travel conditions across higher Pennine and Cumbrian routes, as well as the Southern Uplands, during the early hours of Sunday.
“Temporary blizzard conditions may be encountered above around 300 or 400 metres elevation. These conditions will probably move into some hillier central parts of Scotland during Sunday morning, while snow turns back to rain further south.”
The weather service said areas of Scotland, including Clackmannanshire, Falkirk, Perth and Kinross, and Stirling would be affected.
The yellow warning, which stretches north from England, is expected to end at midday.
On Saturday, the service said it had been a white Christmas for parts of the UK as people in Shetland and eastern Scotland woke up to a blanket of snow.
Aboyne in Aberdeenshire and Strathallan in Perthshire had snowfall overnight.
Video on Twitter, posted by the Braemar, Ballater and Deeside Weather Page, showed substantial snowfall in Braemar.
On Twitter, the Met Office said: “We’ve already seen some snow in Shetland, parts of eastern Scotland.”
The December weather did not stop those wanting a festive dip braving the sea on Christmas Day, including at Portobello Beach in Edinburgh.
And in Montrose, Angus, swimmers also took a dip in the bitterly cold waters on Christmas Day.
Don’t miss the latest news from around Scotland and beyond. Sign up to our daily newsletterhere.