In Shetland, all 47 schools were closed and were due to be closed again on Wednesday. Thirty three schools in Angus were also closed, as well as all schools in Dundee.
Commuters were hit by hazardous driving conditions, while about 15,000 homes were left without electricity after snow and high winds brought down power lines.
More than 300 schools in the Highlands, Grampian, Tayside and the northern isles have closed - many for a second day, with the prospect of further closures on Wednesday.
A train derailed on the Inverness to Edinburgh line at Blair Atholl, leaving 40 passengers stranded for three hours.
Scottish Hydro Electric said engineers have been working to tackle the power cuts, although they faced difficult conditions.
In Tayside and Central Scotland, 3,300 customers were cut off, while another 2,300 lost electricity supplies in the north east and customers in the Highlands were also affected.
By 2000GMT less than 3000 homes were still without power, and less than 1000 were expected to be without supplies overnight.
Thousands of Scottish schoolchildren were given a second day off school.
In the north east, secondary schools which closed included: Alford Academy; Ellon Academy; Inverurie Academy; Mearns Academy; Mintlaw Academy and Fraserburgh Academy.
Exams postponed
Prelim exams due to be taken at Inverurie and Fraserburgh have been rescheduled and a second year parents' night at Inverurie has also been postponed.
Bridge of Don Academy, which had postponed English exams due to be held on Monday, now hopes to hold the exams on Wednesday.
At Mintlaw, prelim exams have been rescheduled to later this month.
Primary schools affected included: Arnage (north of Ellon); Aberchirder; Auchterellon; Auchterlets; Banff; Braemar; Clunie (Sauchen); Craigievar; Daviot; Ellon; Alford and Gordon and Tullynessle primaries and nurseries; Kildrummy; Macduff; Midmar; Logie Coldstone; Luthermiur; Meiklemill (Ellon); Monquhitter; Rothiemay (Moray); Tarland; Torphins; Towie; Glass; Crudie (near Banff); Chapel of Garioch; Durris and Logie Durno (Pitcaple).
In Shetland, all 47 schools were closed and were due to be closed again on Wednesday. Thirty three schools in Angus were also closed, as well as all schools in Dundee.
Schools in the Borders, however, were open.
On the roads, the A9 north of Perth posed problems in both directions due to snow.
On the M90 in the Kinross area, heavy rain and surface water made conditions difficult.
Numerous roads (including A class roads) throughout Perth and Kinross were either passable with care or with difficulty.
Earlier in the day police were advising drivers in the east to use the coast road to and from Aberdeen because of snow on the A90.
Care required
But later they were warning motorists to stay away from the coast road as sections were left under water.
Care was required on roads in the Highlands and Grampian, especially at higher levels.
The A96 between Keith and Fochabers was closed as was the A939 Cockbridge to Tomintoul Road and the A939 Ballater to Gairnshiel Road.
As the snow started to melt further south, flooding affected many parts of Lothian and the Borders later in the day. The A7 and the A68 were among the roads affected.
Inverness and Aberdeen airports were forced to close due to heavy snowfalls but reopened later in the day.
The Aberdeen Exhibition and Conference centre confirmed that Tuesday night's Texas concert was cancelled because of the weather.
The only football fixture to go ahead was the CIS Cup semi-final at Hampden, where Kilmarnock beat St Mirren 3-0.
Meanwhile, more than 100 ferry passengers, who had been bound for Aberdeen, finally disembarked at Invergordon after being forced to stay on board overnight.
The St Clair left Lerwick on Sunday evening but Aberdeen harbour was closed by high winds.
The vessel waited outside the port for 10 hours before leaving for Invergordon.