Strathclyde, Lothian and Borders and Central Scotland police forces advised people not to travel on Tuesday unless their journeys were essential as deep snow and icy conditions have left roads treacherous.
"Due to the extremely cold temperatures experienced across the central belt (of Scotland) overnight, the gritting operation that has been carried out will not have had a significant impact on the ice that has built up on roads across the region," they said.
Temperatures in Scotland dropped well below freezing overnight, and more heavy snow trapped many drivers in their vehicles while others abandoned their cars.
Pupils, parents and staff were forced to spend the night in a South Lanarkshire school after the conditions meant they were unable to get home.
The M876, M80 and M8 motorways were all badly affected and police said they had helped stranded drivers get hotel accommodation or hot drinks and food.
However, Glasgow and Edinburgh airports have both reopened.
Britain, which last year shivered through its coldest winter in 30 years, has not seen such widespread early snowfall since 1993, closing thousands of schools and causing travel chaos up and down the country.