Sally Webb, a forecaster with MeteoGroup, the weather division of the Press Association, said: "Rain overnight across most of southern Scotland will clear and conditions will stay fairly mild for the rest of the week."
Flooding might be a risk in places as the snow melts, the weather experts said.
The Met Office issued yellow "be aware" warnings on Wednesday as up to 2in of snow fell in some areas and up to 6in landed on higher ground.
Several roads were shut as motorists struggled in icy conditions and drifting snow. A man was taken to hospital after a nine-vehicle crash on the A96 in Aberdeenshire involving four lorries, two vans and three cars.
The cold weather is expected to hit again on Tuesday or Wednesday next week.