A yellow "be aware" weather warning is in place for the region, which runs from 8am on Thursday until just before midnight.
The wintry weather follows snow and cold temperatures experienced in parts of Scotland earlier this month.
On Saturday the heaviest and most frequent of the snow showers will progressively become confined to northeast Scotland with strong northwest winds possibly causing drifting of the snow in places with blizzard conditions possible.
'Overnight, the main feature will be the increase in wind as Caroline starts to come in towards the end of the night.
Elsewhere, aound two inches of snow is forecast to fall in across many other parts of Scotland, Northern Ireland, Wales and western England.
Roads, railways and ferries are all expected to be disrupted as gusts of 70mph to 80mph are hit northern Scotland, increasing to 90mph in exposed areas.
Friday will also be cold, Met Éireann said, with sunshine and scattered rain, hail, sleet and snow showers, and temperatures of 3 to 6 degrees in gusty northwesterly winds.
A Met Office spokeswoman, Nicola Maxey, said: "Winds will pick up across the rest of the country so it will be a blustery day for many areas".
"On Thursday, the strength of the wind during the morning peak period is likely to lead to bridge restrictions and closures and we would urge drivers to check ahead", said Transport Minister Humza Yousaf.
Offaly is now covered by a fresh snow-ice warning from Met Éireann.
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