It said accumulations of up to 20cm (8in) were likely, mainly above 400m but possibly as low as 300m, with drifting caused by strong easterly winds.
Main routes which could be affected include the A9 around the Drumochter pass, the A82 north of Tyndrum and the A87 west of Invergarry.
The agency warned: “The public should be aware of the risk of difficult driving conditions on higher roads.
“In addition, conditions are likely to be hazardous for those out on the hills and mountains, whilst heavy rain at lower elevations may lead to surface water on roads.”
Heavy rain is forecast to spread north east across Scotland tonight, with snow above 300m and drifting caused by strong easterly winds.
A Met Office spokesman said: “An active front will encounter cold air as it pushes into Scotland, with rain turning to snow over high ground.
“Winds will increase, gusting to over 50mph on hills, and causing snow to drift.
“There is a fair amount of uncertainty about just how low snow will penetrate, and whether it will affect road levels.”
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