It follows a spell of unseasonably warm weather, which saw the mercury hit temperatures of 24 degrees across the country last week.
According to forecasts, rain will southwards tonight (Monday) and into Tuesday.
The warning for the Strathclyde region will remain in force until 11am on Tuesday.
A spokesman for the MET office said: "Rain will turn increasingly to snow which will settle mainly on hills above about 200m.
"Here accumulations of 5 cm or so are expected in places, whilst a mixture of rain, sleet or snow at lower levels brings the risk of some temporary slushy accumulations. "The public are advised to be aware of the risk of some disruption to transport."
For more information visit http://www.metoffice.gov.uk.