People have been urged to continue to travel with caution as Scotland gradually recovers from the impact of last week’s severe weather.
Met Office yellow warnings for snow and ice remain in place for large parts of the country.
Thousands of school pupils are expected to begin returning to their classrooms later.
The Scottish government said people could still expect to face “challenging” conditions in some areas.
Most councils said they hoped to reopen the majority of their schools on Monday, however people were urged to check their council websites and social media feeds for information on individual schools.
Scottish Borders Council said 19 rural primary schools would remain closed on Monday morning and secondary schools would only reopen for S4-S6 pupils.
Fife Council decided that all schools and nurseries would stay shut on Monday.
The west coast mainline between Scotland and Carlisle reopened on Sunday evening after several days with no trains running.
ScotRail said on Sunday that the rail network was back to running a “near-normal” service.
The yellow weather warning in place for Monday covers Central, Tayside and Fife, Grampian, Highlands and the Western Isles, Orkney & Shetland, south west Scotland, Lothian, Borders and Strathclyde.
A further warning, which runs until 15:00 on Tuesday is for Central, Tayside and Fife, Grampian Highlands and Western Isles and Strathclyde.
Deputy First Minister John Swinney said: “Conditions have improved significantly in many parts of the country but I would urge the Scottish public to remain vigilant.
“Yellow (be aware) weather warnings are still in place across all but the most westerly parts of Scotland, and in most parts ice and surface water will create challenges for drivers on some minor roads.
“The advice from Police Scotland is travel with caution in all areas, and drivers are encouraged to plan ahead and check weather forecasts.”
The country ground to a halt last week as heavy snow falls prompted a red weather warning and the public were urged not to travel.
Pupils across much of the country spent at least three days at home as schools were closed.
Businesses were also affected with shops and offices forced to close and employers urged to allow staff to work from home.
On Sunday, Transport Minister Humza Yousaf told BBC Scotland he would be considering action against employers for docking the wages of staff who could not make it to work during the most severe weather.
He said it was “unacceptable” after he was contacted by people who were facing disciplinary action or potential docking of wages.
Over the weekend, “armies” of volunteers gathered to clear snow from local roads and playgrounds in a bid to get Scotland back to work and school as normal.
The economic impact of Scotland’s big freeze is also now being considered.
On Sunday, a leading economist warned it could run to hundreds of millions of pounds.
Over the weekend, shops in snow-hit areas were beginning to restock their shelves with essentials after running short of supplies.
However, many customers still faced empty shelves and some stores were rationing bread and milk as they waited for fresh deliveries.
BBC contributed to this report.