Dumfries and Galloway has been worst-hit by the treacherous conditions, with police in the area advising motorists to stay off the roads.
The force said drivers could face severe delays of up to several hours.
Up to 10 inches of snow has already fallen in exposed parts of the region, where more than 100 schools were closed today.
Forecasters have said there is more wintry weather to come for most of the country.
The south-west of Scotland and the Lothians and Borders area have been issued with an amber "be prepared" warning from the Met Office while the Highlands and Western Isles, Grampian, Strathclyde, Tayside, Fife and central Scotland areas are on yellow "be aware" alerts.
The warnings are in place until midnight on Saturday.
Thirty-five schools are closed in Aberdeenshire, 10 in Argyll and Bute and 16 across Ayrshire, as well as Dyce Academy in Aberdeen and both Dalgety Bay nursery and primary school in Fife.
Dumfries and Galloway Constabulary said: "Conditions for travel are extremely dangerous and you should avoid the specified roads, and if you do travel you will experience severe disruption.
"Congestion caused by vehicles may restrict emergency, recovery or winter maintenance vehicles from providing essential assistance or from clearing roads.
"Drivers of HGVs should drive with extreme caution and be aware that you may be requested to park at a suitable position by the police.
"Winter driving is a question of common sense and drivers should ask themselves if they really need to travel when conditions are poor."
A number of roads in the region are closed or partially disrupted by snow, including the A77 between Stranraer and Portpatrick, the A709 between Dumfries and Lochmaben, the A711 at Longwood and a stretch of the A74(M) between junctions 17-19, where diversions are in place.
A police spokeswoman said there have been a number of accidents but there are no reports of any serious injuries.
Tayside Police also asked drivers to take extra care in the area, with drifting snow causing some disruption.
It said people should make sure their mobile phones are fully charged before travelling and to make sure they have enough fuel, food and water to last them in the event they are delayed for a long time.
The force said: "In Angus, motorists are advised to avoid the Wellbank and Craichie areas following high winds and drifting snow which have made roads impassable.
"Road closures are in place on the B9128 Forfar to Arbroath Road, B978 Kellas to Kirbuddo Road and all unclassified roads within the area.
"They will be closed for some time as high winds and drifting snow continue to affect these roads."
Laura Caldwell, a forecaster for Meteogroup, said: "There is snow mainly across the south of Scotland, which is creeping into the west, with some scattered showers also affecting the east of the country.
"The north west has the best of the weather where it is mostly dry, with the south really getting the brunt of it.
"That's the way it will stay overnight, easing off tomorrow.
"By Sunday it will turn into more of an easterly wind, with some better weather in western parts of the country and snow showers in the east.
"Over the next 24-48 hours there could be about 10-15cm accumulations over higher ground, but most of that will fall during the darker hours."
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