The agency said frequent snow showers are expected to continue into early Wednesday while severe gale force winds would create “dangerous coastal conditions” from large waves.
Travel disruption is expected, especially on higher-level roads.
It comes as a separate yellow warning, for gales of up to 75mph, remains in force for much of the Hebrides until 5pm today.
A Met Office spokesperson said of the snow warning: “Showers, accompanied by strong winds, will become increasingly frequent and wintry through Tuesday at all levels, before dying away Wednesday morning.
"Below 100m, accumulations are most likely to be temporary and slushy.
"Greater likelihood of more significant accumulations (2-5cm, and in places 10-15cm) above 200m.
"In combination with winds gusting 50 to 60mph, perhaps 70mph on exposed summits, temporary blizzard conditions and some drifting of snow on higher level routes is likely.”
Major routes above 200m which could be affected include sections of the A96 around Huntly and Keith, the A95 between Aviemore and Craigellachie, the A9 between Dalwhinnie and near Inverness, the A97 west of Invergarry, and a stretch of the A835 Garve-Ullapool road around Loch Glascarnoch.
The Met Office spokesperson added: "Gusts of around 70mph on exposed coasts will generate some large waves and dangerous coastal conditions in a few places.”