Rail routes remained largely unaffected but there were several flight cancellations between London City, Heathrow and the East Midlands to Aberdeen, Glasgow and Edinburgh airports.
Borders Council said 17 schools were closed but are set to reopen on Tuesday along with others in Aberdeenshire, Angus, Perth & Kinross and Moray.
Tony Conlan, a forecaster with Meteo Group, the weather division of the Press Association, said: "Most of the snow has been falling in the southern half of Scotland, probably heaviest in the Borders, where there has been about 9cm of new snowfall in Eskdalemuir.
"The snow will continue intermittently through the night, pushing north leaving only the west of the country dry."
Scottish transport minister Keith Brown said commuters should continue to plan journeys carefully.
