The Met Office has issued amber weather warnings for eastern Scotland, urging the public to be prepared – including alerts for the Borders, north-east Fife, Perth and Kinross, Angus, Aberdeenshire and Moray.
Heavy snow is expected, with up to 20cm on higher ground, and strong winds are also forecast with potential for drifting snow. A number of existing yellow "be aware" warnings also remain in place across the rest of the country.
The big freeze that has gripped much of England and Wales is expected to hold until Thursday. Across Strathclyde today, it will be cloudy with outbreaks of snow – which will be stronger in Lanarkshire – with strong easterly winds.
Transport Minister Keith Brown said: "As the wintry weather continues, Transport Scotland stands ready to respond swiftly and appropriately.
"Motorists and public transport users should factor the weather and high likelihood of disruption into their travel plans, staying abreast of live travel information.
"While we have implemented a raft of improvements ranging from higher than ever salt stocks to a strengthened fleet of gritters, the public must play their part by making full use of the vast sources of communications available."
He added: "Drivers should take the road conditions into consideration, leaving extra time for journeys if necessary.
"The Traffic Scotland Control Centre continues to monitor the travel situation very closely and the website, Variable Message Signs and internet radio will be used to provide up-to-date information as the situation develops."
Assistant Chief Constable Allan Moffat, speaking on behalf of the Association of Chief Police Officers in Scotland, also urged motorists and commuters to regularly check weather and travel reports.
He said: "Weather warnings are in place for many parts of the country, particularly in the east. If you are travelling, be prepared for the winter weather.
"Check conditions and travel advice before setting off and ensure that both you and your vehicle are adequately prepared for the journey.
"Allow yourself plenty of time and make sure that you have sufficient fuel and supplies such as warm clothing, food and water in case you are delayed. When you are out on the road, remain vigilant and continue listening to weather and travel reports."
The rest of the UK has already felt the full force of the wintry weather, with reduced train services and cancelled flights.
A total of 260 flights were cancelled at Heathrow Airport yesterday, 20% of the sites usual business, with around 10% expected to be cancelled today due to poor visibility.
The Heathrow Connect and Heathrow Express train services were also hit by major delays to and from the airport.
The Met Office added temperatures are expected to rise towards the end of the week.
l A MAN and his seven-year-old daughter both suffered broken legs in a sledging accident in the Scottish Borders.
The pair lost control of their sledge going down a hill in Selkirk and collided with a park bench.
An ambulance crew attended the incident, which happened at around 2pm on Saturday.