A spell of rain, sleet and hill snow will move northeast on Saturday evening, this gradually turning to snow down to some lower levels.
Clearing skies later in the night will lead to ice developing on untreated roads, pavements and cycle paths.
Frequent, heavy hail and snow showers are expected through Sunday and will lead to snow accumulating on many surfaces.
Longer journey times by road, bus and train services are likely while some vehicles could become stranded.
Ice is likely to form on untreated pavements, cycle paths and roads leading to some injuries from slips and falls.
Power cuts may occur and other services, such as mobile phones, may be affected.
Met Office Chief Forecaster said: “A very cold westerly airstream will bring frequent snow showers to many western and central areas on Sunday.
“2-5cm of snow may accumulate above 150m with some snow to low levels too.
“10cm or more is possible above 300m, with drifting in the strong westerly winds.
“Ice will also be a hazard overnight into Sunday morning and then is expected to return in the evening.”