The Met Eireann Yellow Status alert has also been issued for for Connacht, Clare, Cork, Kerry and Limerick.
The forecaster says it will be bitterly cold overnight with scattered snow showers, mostly affecting Donegal leading to accumulations of 1 to 3 cm in some areas, most especially on higher ground.
There is also a widespread frost alert with overnight lows of 0 to -3 degrees Celsius.
The alert remains in place until 11am on Thursday.