Some areas may see as much as 13cm of snow on the ground as Arctic conditions sweep across the country.
Temperatures will also drop to below freezing and rain today will turn to snow later in the evening. Central Scotland and the Highlands are the areas expected to be worst hit.
Forecasters said the weather was not expected to be as bad as the blizzards that hit most of the country at the beginning of last month, resulting in chaos on the roads and the closure of hundreds of schools. Milder weather is likely to return by week's end.
Paul Mott, forecaster for MeteoGroup, the Press Association's weather division, said: "Through Tuesday it will be cloudy and chilly with outbreaks of rain and sleet.
"Later in the afternoon we're expecting snow over the hills in central and western parts of Scotland.
"During the evening that snow will become heavier and will start to fall at lower levels too, most likely over central and northern parts of Scotland."
He added: "Places like Glasgow will see a few centimetres through the evening but not a significant amount.
"The worst of it will be between 6pm and midnight and will gradually clear out to the North Sea."
He said higher ground may see 13 centimetres of snow while lower ground in central and the north can expect 5 or 6cm.
Forecasters also confirmed that Britain has had its coldest winter for more than a decade. The last three months have been the chilliest for 13 years, with an average temperature of 2.9C.