Yesterday's snowfall was mostly melted by later rain, only to be turned into ice as the temperature dropped below zero in the early hours.
The Met Office had a weather warning in place for icy conditions over much of Scotland until 11am.
Forecasters also warned of more snow to come in central, northern and eastern parts of Scotland tomorrow.
The warning came after around 4cm of snow fell across the West of Scotland on Sunday night,.
Disruption on the main transport network was kept to a minimum, and the Scottish Government confirmed they were on alert to respond to any major problems.
Charlie Powell, forecaster with the Met Office, said: "There were quite a few snow and sleet showers in the West of Scotland yesterday.
"They continued throughout the day and turned to snow on higher ground.
"It is definitely going to be on the frosty and icy side and conditions are expected to stay like this for the rest of the week."
In Glasgow, the ice-rink in George Square, set up as part of the city's festive campaign Glasgow Loves Christmas, was forced to close because of a flurry of snow.
The facility closed at midday yesterday and opened again around two hours later.
Transport Scotland was preparing to respond to any major problems.
A Scottish Government spokesman said: "We are continuing to monitor the situation.
"We have seen a wide range of agencies working together to put in place their response plans.
"The travelling public also deserve praise for the way they have behaved.
"However, no one is being complacent, and whilst the weather alerts remain in place, the focused response will continue."