Motorists have been urged to take care after further warnings of heavy snow on high grounds in eastern parts of Scotland.
The Met Office said that eastern Scotland, especially the Borders, Angus, Perthshire and Aberdeenshire could have up to 10cm (4in) of snow.
They warned that driving conditions in these areas could be hazardous.
Severe snow in England has continued to disrupt flights and passengers were advised to check with airlines.
The west of Scotland should escape the worst of the icy blast, with snow probably turning to sleet.
Scottish Borders Council confirmed that all 74 schools in the region would be closed on Tuesday as a precaution.
Snow falls in Scotland did not cause the disruption seen in London and the south of England on Monday.
However, problems at southern airports including London City, Stansted and Gatwick led to the cancellation of at least 132 flights in and out of Scotland.
All British Airways connections to Heathrow were cancelled as the heaviest snowfall to hit the UK capital in 18 years brought the hub to a standstill.
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Some flights to Heathrow were being diverted to Prestwick in Ayrshire.
The manager of Prestwick airport said it handled about 1,500 extra passengers.
Passengers on the services from the United States, the middle east and the far east were being put up in local hotels overnight.
The airport's CEO Mark Rodwell said: "Hotel accommodation is being arranged on behalf of the airline for the disrupted passengers, with most being accommodated in the local area.
"Some passengers have elected to make their own alternative arrangements via hire cars or rail.
"We are waiting to hear from British Airways regarding flight arrangements for Tuesday."
Mr Rodwell said the airport's own schedule had been largely unaffected.
Heavy snow showers hit parts of the Scottish Borders
Edinburgh Airport was closed for more than an hour on Monday evening due to snow on the runway.
A BAA Scotland spokeswoman said: "The airfield operations team worked hard to clear the runway, which is now open to both inbound and outbound flights."
Passengers intending to travel from Scotland were advised to check with their airline before leaving for the airport.
Heavy snowfalls closed roads in north east Scotland.
The A93 Braemar to Spittal of Glenshee road and B974 Banchory to Fettercairn road were both shut.
Grampian Police said the A939 Cockbridge to Tomintoul route was also closed because of heavy snow.
Conditions on other roads in the area were treacherous and the force warned drivers to think carefully before getting behind the wheel.
In Kelty, Fife, two members of an ambulance crew were taken to hospital after their vehicle overturned in snowy conditions.
The vehicle skidded as they drove along the A909 on their way to an emergency call on Monday morning.
However, despite the cold snap, Inverurie Locos' Scottish Cup fourth-round tie against Motherwell went ahead at the fifth time of asking.
The Harlaw Park pitch passed an inspection on Monday morning after the tie was called off on four occasions due to the frozen pitch.
The Aberdeenshire side lost the tie.
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