The Met Office said Tuesday would be cold and cloudy with some snow during the morning, leading to slight accumulations. Long clear spells will occur in near calm conditions allowing a few mist and fog patches to form.
Rain will develop in the west this afternoon, which will spread eastwards through the evening and early night, turning to sleet and snow.
He said that the snow will not be excessive but frost overnight could cause hazardous road conditions.
The outlook is for conditions to be cold and clear with sunshine on Wednesday, ahead of a cloudier and breezier Thursday with a little rain and sleet.
"Tomorrow morning will see wintry showers of sleet and snow", he continued. Met Eireann expects lowest temperatures of -2° to 1° tonight. Drier and brighter weather is forecast in the east and south-east, however.
The temperatures will hit highs of 5C in some areas of the country, with fresh, gusty, northwest winds.
It is expected that temperatures will fall to -4C overnight with a widespread frost and the risk of ice on untreated roads and other surfaces.