The yellow warning will remain in force until midday today.
Forecasters said showers accompanied by widespread sub-zero temperatures would see ice form on many untreated roads.
Some snow is expected even at low levels in northern Scotland and other areas could see 2-3cm fall on higher ground.
A Met Office forecaster said: “Over northern Scotland showers will fall as snow to low levels.
“Elsewhere within the warning area these showers will be turning increasingly wintry, with the main snow level down to between 100 and 200m by the end of the night.
“Locally 2 or 3cm of snow is possible above 200m.”
Heavy snow covered large parts of northern England on Friday and Storm Jake is now moving slowly down the country.