Traffic Scotland has issued a warning to motorists of icy conditions on the roads in Grampian, Highlands and Western Isles, Central, Tayside, Fife, Lothian, South Scotland and Strathclyde.
The cold weather is expected to continue into the week with some temperatures in the UK expected to drop to -6, according to the Met Office.
Traffic Scotland posted online: "Road users are advised to drive with care due to low temperatures and the risk of ice currently affecting driving conditions on many roads throughout the region. has been cleared."
The 1,000-mile wide cold air plume will bring Scotland's coldest week since early December, after -5C (23F) nights.
5-7C highs will be around average, but feel bitter after a month of often balmy above-average temperatures.A Met Office forecaster said: “After Monday's cloud, from Tuesday to Thursday sees low cloud for the North-West and bright conditions at times in the North-East.
“Into the weekend stays cloudy for most. Into the following week, the North could be wetter and windier at times.”
Ex-BBC and Met Office forecaster John Hammond of weathertrending said: “Chiller air is following.”
Dr Owen Landeg, an environmental public health scientist, said: "Below 18 degrees, changes to the body mean that the risk of strokes, heart attacks and chest infections increase so heating homes to this temperature is particularly important to stay well."
The cold snap comes after Storm Brendan swept across parts of the UK last weekend causing road closures and rail disruption, as well as gales of up to 80mph.
It also marks a change from last month when meteorologists confirmed that a new UK maximum temperature record for late December was set in the Highlands. A temperature of 18.7C (65.66F) was recorded at Achfary in Sutherland on December 28. The reading was validated following a "rigorous verification process", the Met Office said.
Asked why temperatures have dropped, Mr Wilson said: "It's all to do with the pressure pattern and it also depends on how high or low the pressure is. Right now there is cold air sitting directly on top of the UK and there is high pressure coming from the north and the east."
More as we have it.