A Met Office yellow "Be aware" warning predicts icy patches on untreated roads and pavements during this morning's rush hour.
It follows a day of chaos yesterday, when a lorry jack-knifed on the A8 in Lanarkshire and closed a main Glasgow to Edinburgh route.
A number of schools were closed in South Lanarkshire, where the council also suspended school bus travel for pupils with special needs.
Nicky Maxey of the Met Office said: "It is going to be very cold in Scotland overnight with -5C (23F) in Glasgow and -3C (26F) in Edinburgh.
"Many places had snow today so that melting and then freezing will be enough to cause difficult driving conditions in the morning."
Lanarkshire appeared to suffer some of the heaviest snowfalls yesterday. Police dealt with a series of road accidents in the Lanark area.
Glasgow-bound commuters were brought to a halt due to a lorry getting stuck in snow at the Kingsgate Retail Park in East Kilbride.
Scots commuter face a second day of treacherous driving conditions tomorrow
The local authority said seven schools and nurseries were closed with children at a further 11 schools told to come to school later.
It is going to be very cold in Scotland overnight
South Lanarkshire's head of roads, Gordon Mackay, defended his department against accusations from drivers that roads had not been gritted. He said: "Gritters were out on all main gritting routes from 3pm on Monday.
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The Met Office predicts icy patches on untreated roads and pavements SNOW UK 2017: All the amazing images so far Fri, February 10, 2017
Many places in the UK have been hit by snow. Blustery and wintry weather will sweep across Britain bringing fears of disruption and travel chaos.
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A snowy scene on the North Yorkshire moors, as a mini cold snap brought snow to parts of the UK.
"These continued to patrol and treat through the night, and all roads were clear until about 5am when significant snow began to fall.
"Such heavy snowfall immediately before and during the morning rush hour will inevitably cause difficulties, as it will lie on roads, including those that have already been gritted.
"It takes the action of vehicle tyres with the salt to generate a melting effect, as well as further ploughing to clear it.
"During rush hour periods this is particularly challenging, and we continue to urge road users to drive to the prevailing conditions."
Roads in other parts of Scotland were also badly affected.
A main Glasgow to Edinburgh route was closed today after a lorry jack-knifed on the A8
Nicky Maxey of the Met Office said it 'is going to be very cold in Scotland overnight'
The main A8 road between Glasgow and Edinburgh was blocked for several hours west-bound at Newhouse in Lanarkshire. There were long delays in Ayrshire on the
M77 southbound due to a crash at Kilmarnock and north bound due to an accident at Junction 6 Kingwell.
The A83 at the Rest and Be Thankful in Argyll was closed for a while and even after it reopened police described conditions as "precarious".
The A702 near Penicuik in Midlothian was closed between Flotterston and Mauricewood due to what Transport Scotland described as "multiple road traffic collisions".
There was only minor disruption on the railways, mainly on the Edinburgh to Aberdeen line due to a breakdown at Leuchars.