Temperatures are predicted to fall as low as -14C, beating -10.8C at Braemar in Aberdeenshire on 18 January.
Edinburgh was expected to dip to -5C and Glasgow to -4C.
A yellow - “be aware” - ice warning remains in force for western Scotland until 11am.
It will be followed by a snow and ice alert for eastern Scotland from 6pm until noon on Friday.
The Met Office said wintry showers would become more frequent tomorrow morning.
A yellow warning for the east tonight, which also covers northern Scotland, will see up to 3cm of snow, according to the Met Office.
It said: “Showers will develop during Thursday night and continue into Friday morning falling as a mixture of rain, sleet and snow. “Snow accumulations of 1-3cm are possible in places.”
Network Rail has prepared for any disruptive snowfalls by moving seven snowploughs and snowblowers into position across the Scottish network “as a precaution”.
However, it said the main concern was freezing temperatures causing points between tracks and signals to stop working.
Forecast temperatures for tomorrow night and Friday have been revised downwards in some areas, with -4C expected in Glasgow tonight and -3C on Friday night. Edinburgh is still on for -2C for both nights.
However, at Loch Glascarnoch, north west of Inverness, the temperature did not rise above -1C today – the coldest place in the UK. The deepest snowfall recorded today was 11cm at Tulloch Bridge, east of Fort William.
The Met Office said: “It will stay cold into the weekend with wintry showers, particularly in the north and east of the UK.
“Further warnings of snow and ice may be required.
“During Sunday and Monday, bands of rain and snow look likely to arrive from the west.”