The yellow warning covers the period from 4am until noon today.
Up to 15cm of snow is expected to fall across high ground in parts of Scotland and up to 2.5cm could affect lower areas.
Rain may also fall onto frozen surfaces for a time, which could result in very icy conditions.
The snow will turn to rain again as much milder conditions follow from the southwest by the afternoon.
A spokesman for the Met Office said: “Rain is expected to turn to wet snow with 2-5cm possible above about 150m, and some slushy accumulations possible at lower levels. 10cm may possibly occur above 300m.
“Please be aware of the need to take extra care and allow more time for travel.”
Drivers faced delays on all four of Scotland’s main north-south routes on Sunday, when motorists were advised to avoid the A82 for a time after jack-knifed lorries at Tyndrum led to cars becoming stranded.
The official Traffic Scotland information service said that at one point no traffic was moving on the A90 north of Dundee because of lorries stuck northbound and multiple accidents southbound. Cars were also reported to have become stuck at Dunkeld on the A9. The roads were later cleared.
The A93 was closed between Braemar and Glenshee.
Elsewhere, flooding caused driving hazards, with long tailbacks reported on the A90 at Cramond Brig in Edinburgh. Other routes affected included on the M9 east of Polmont, the M90 south of the Forth Road Bridge to the M9, and the Clydeside Expressway in Glasgow.
Strong winds closed the Erskine Bridge over the Clyde and Skye Bridge to high vehicles.
Wind speeds reached 75mph at Dundrennan, near Kirkcudbright in Dumfries and Galloway.
Cross-Border trains on the east and west coast main line were delayed by high winds leading to speed restrictions. Fallen trees caused further problems on the west coast route and tree branches blocked the Glasgow-Dumfries line at New Cumnock in Ayrshire.
CalMac cancelled ferry sailings on several routes, including on the main Arran service between Ardrossan and Brodick, and Oban to Mull.
Cambuslang in South Lanarkshire and Kilmarnock in East Ayrshire cancelled their Christmas lights switch-ons last night because of strong winds.
The Met Office said 10-15cm of snow could accumulate over some high ground areas by this morning, especially in the west Highlands.
A spokesman said: “Further clusters of heavy wintry showers will come in from the west, even extending to parts of southern Scotland on Sunday evening and at first on Sunday night, leading to further accumulating snow in places, especially the west Highlands.”