The Met Office has upgraded its weather warning to severe amber level and indicated that heavy snow with blizzards could lead to travel delays and power cuts across parts of the country.
The central belt, Borders, Dumfries and Galloway, southern parts of Tayside and Fife are anticipated to be affected until Sunday morning.
An amber warning for snow is also in place across Stirlingshire, Perthshire, parts of Grampian and the southern Highlands.
Police Scotland said people should only travel if they consider it necessary.
A statement read: “Winter driving is a question of common sense and all drivers should ask themselves if they really need to travel when conditions are poor.
“No-one should ever place themselves at risk on the road and it may be worth making alternative arrangements such as delaying travel until conditions improve, or using public transport.
“If you are travelling on the roads you should ensure you and your vehicle are adequately prepared for the conditions, making sure you have sufficient fuel and supplies such as warm clothing, food and water in the event you are delayed for several hours.
“Charge your mobile phone and plan your route as well as alternative routes.”
Following a meeting of the Scottish Government’s Resilience Room on Friday, Transport Minister Michael Matheson said delays and cancellations on public transport were possible.
There could also be interruptions to power supplies and telephone networks, and some rural communities may find themselves cut off.
Mr Matheson said: “I would encourage people in the affected areas to consider whether they need to make their journey. If they do, they should expect disruption.
“Drivers should plan their routes, leave plenty of time, follow Police Scotland travel advice and drive to the conditions.”