In Orkney, an ambulance crashed on to its roof in what police described as "atrocious" conditions.
The vehicle, with two people on board, left the main Kirkwall to Stromness road. One of the crew members was taken to hospital for treatment.
Grampian Police urged drivers to stay off roads across the north east unless journeys were "absolutely necessary" and to leave work early.
The A90 south was passable with extreme care and was down to a single lane.
Conditions on the A96 between Inverurie and Aberdeen were said to be deteriorating in the afternoon and motorists were urged to avoid it.
Drivers were also asked to avoid the A920 Pitmedden to Ellon road due to treacherous conditions.
Journeys to work in Aberdeen's morning rush hour took far longer than usual due to congestion in the snow and icy side roads.
At one point the whole of Anderson Drive was shut, leading to major delays.
Drivers had to dig cars out of snow to start journeys
Aberdeen City Council urged drivers to treat gritters like emergency vehicles and let them through the traffic.
There was widespread disruption to flights from Scotland's airports due to weather conditions in England.
Passengers were advised to check with their airline before travelling to airports.
Police in Edinburgh said roads were passable with care.
In 24 hours Edinburgh City Council said it had used almost 500 tonnes of pure rock salt on the capital's roads and paths.
The Forth Road Bridge had a reduced speed restriction of 30mph for an hour from 0700 GMT on Tuesday due to heavy snow.
Workers have been de-icing the carriageway using a chemical called Glycol because they cannot use the normal method of salt as it would corrode the steel bridge.
Dumfries and Galloway Constabulary also warned of dangerous driving conditions across its force area.
The A75 between Newton Stewart and Stranraer was badly affected by snow and ice overnight but was said to be passable with care.
Black ice caused major problems on the A714 from Newton Stewart to Wigtown.
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