New amber alerts for snow have been issued by forecasters, covering much of northern Scotland, starting on Sunday evening.
The Met Office said another 5-10cm (2-4ins) could fall fairly widely in the north east, Highlands and Northern Isles while a few places on the mainland could possibly see 20-30cm (8-12ins).
Widespread snow accumulations in recent days have already led to treacherous driving conditions with numerous reports of vehicles getting stuck.
The new alerts, which also warn of strong winds, run from 18:00 and continue until 10:00 on Monday when many schools are due to reopen after the holiday. Some councils have already announced closures.
A yellow warning for snow and ice is in place for areas north of Glasgow and Fife, with a second warning covering parts of East Lothian and the Scottish Borders on Monday and Tuesday morning.
Highland Council said road conditions in Easter Ross, Sutherland and Caithness were particularly challenging, with drifting and freezing conditions overnight, and it advised people to travel only if it was essential.
The A9 and A99 between Helmsdale to Wick remained closed due to heavy snow, poor visibility and drifting.
Some 32 gritters were sent out in Aberdeenshire on Sunday morning but parts of the road network were still said to be “impassable”.
Vehicles were struggling in difficult conditions on the AWPR bypass that wraps around Aberdeen on Sunday.
Network Rail said heavy snow in areas such as Kintore in Aberdeenshire, had seen snowploughs dispatched to clear the railway line, as well as further north on the line to Wick.
One of its snowploughs encountered drifts up to 1.2m (4ft) deep near Laurencekirk.
Train operator ScotRail said it was unlikely to be able to run services between Aberdeen and Inverness, Aberdeen and Dundee and Inverness-Wick/Thurso services until at least midday.
Loganair has cancelled a number of Sunday flights but Aberdeen Airport remained open.
A spokesperson said: “With weather warnings in place we urge passengers to check the status of their flight with their airline before they travel to the airport.”
Sunday flights in and out of Sumburgh Airport in Shetland have been cancelled
All schools in Shetland will be closed on Monday as a result of the amber warnings.
Aberdeen City Council has said the reopening of its schools would be delayed until 11:00 on Monday due to uncertainty about the weather conditions, and breakfast clubs will not open.
Further updates for each school will be issued by head teachers on Monday morning, it added.
A number primary schools in Moray will be closed, with arrangements for home learning put in place.
Transport Scotland said a multi-agency response team would have extended operating hours to monitor conditions and co-ordinate various agencies.
Asst Chief Constable Alan Waddell of Police Scotland advised people to consider if journey were absolutely necessary during the weather warnings.
He added: “If you need to travel, please drive to the conditions, be prepared for delays and allow extra time for your journey.
“Please don’t drive through road closures, the decision to close roads is not taken lightly and is done for public safety.”