Teams of experts spent all day working on roads, with the north-east expected to be one of the areas worst affected by snowfalls.
Extra staff were called in for overnight and early morning operations as snow was expected to fall from midnight until 7am this morning.
Motorists were urged to allow extra time for journeys in the morning and be dressed appropriately for the conditions.
The Met Office's yellow "be prepared" weather warnings are in place for Grampian, Central, Tayside, Fife, Lothians, the Borders, Strathclyde, the Highlands and south-west Scotland.
Vehicle owners were also being asked to ensure that, if they park on roads, they leave plenty of space for the gritters and ploughs, which are fitted with a three-metre-wide blade, to manoeuvre past.
An Aberdeen City Council spokeswoman said: "The teams are working long hours in bitter conditions to treat as many surfaces as possible.
"Aberdeen City Council would like to remind residents that the grit bins on city streets are available for all to use.
"Residents are reminded the grit is there for them to use on public areas, as well as for the use of council staff."
Heavy snowfall in parts of the country has disrupted some pupils and teachers returning to school after the weekend.
Around 3cm of snow fell in parts of eastern Scotland over six hours, forecasters said.
Several schools in Aberdeenshire and the city were forced to close or end the day early, while others had transport disrupted.
Ice and snow warnings remain in place for large parts of the country.
In Aberdeenshire, Chapel of Garioch School Crathes School and Towie School were shut.At least six schools or pre-school services in Aberdeen announced partial closures, according to the city council. .
Motorists were advised not to travel on the B976 Crathie to Gairnshiel road and that the B977 Dyce to Fintray road was only suitable for 4x4 vehicles. The B974 Banchory to Fettercairn road was closed.
A car left the road near Forres and another near Aboyne, but there were no serious injuries.
The first widespread snow of the year fell over the weekend and there were further accumulations in the north and east of the country yesterday.
Sean Penston, a forecaster with Meteogroup, said eastern areas and higher ground have had quite a few snow showers.
Temperatures were expected to fall to minus 4˚C in some eastern parts last night, he said.
Meanwhile, the AA said 75% of drivers are not prepared for conditions on the roads and urged drivers to carry a winter kit and to check their cars before getting behind the wheel.
Transport Minister Keith Brown said: "While the Met Office predicts Scotland is expected to escape the most severe weather in other parts of the UK, I would ask the public to remain vigilant and drive to the conditions."