Up to 8cms of snow is also forecast, with two weather warnings in place
Temperatures are due to plummet to -5 degrees tonight, as the freezing conditions continue.
Motorists are being advised to drive with extra care.
An orange snow-ice warning remains in effect for counties Donegal, Leitrim, Mayo and Sligo - with snow accumulations of between 4cms and and 8cms possible.
While a yellow warning for snow and ice is also in place for Longford, Cavan, Monaghan, Galway and Roscommon.
Met Éireann says up to 4cms of snow could fall in these areas.
Overall it is very cold this morning with frost and icy patches, but with many areas dry.
However showers of sleet or snow are continuing in west Munster, Connacht, Ulster and north Leinster, becoming more isolated later.
They will persist in the north, falling as rain or sleet this afternoon, and rain or drizzle is also expected in the southwest later.
Tonight will be dry apart from some patchy rain or drizzle in the southwest - but very cold with clear spells and patches of freezing fog.
There will be a severe frost with icy stretches on roads and lowest temperatures of -5 to +2 degrees, coldest in the south midlands and least cold in the southwest.
Gerry Murphy from Met Éireann has the outlook.