Met Éireann has warned that overnight temperatures will drop to as low as -6C.
It said it will continue to be very cold until the weekend with severe frosts at night and ice on untreated surfaces.
Many local authorities gritted roads today as the Status Yellow snow and ice weather warning remains in place until Sunday.
It was cold overnight. Temperatures at some of our weather stations at 6am.
— Met Éireann (@MetEireann) January 31, 2019
Dublin Airport: - 5.8C
Mullingar: -4.8C
Mount Dillon: -4.0C
Oak Park: -3.7C
Ballyhaise: -3.4C
Grange: -3.1C
Gurteen: -2.7C
Shannon Airport: -2.7C
Moore Park: -3.4C
Phoenix Park: -3.9C
Casement: -3.0C
Meteorologist with Met Éireann, Harm Luijkx, said there would be accumulations of snow on higher ground, in particular in Co Wicklow.
He also said there would also be accumulations tonight on lower ground in the south of the country.
Mr Luijkx said this band of weather would move south overnight and that tomorrow would be a drier day.
Last night, as temperatures dropped to as low as -4C in some areas, there were reports of very icy road conditions in Cork, Limerick, Galway, Tipperary and Roscommon.
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Local authorities in affected areas said they gritted the main roads last night and would do so again today.
Schools bus services did not operate in a number of areas in Donegal including Carndonagh, Moville, Killybegs and Bundoran.
Motorists were warned of icy conditions this morning and heavy rain later, with rain also turning to sleet and snow for a time over parts of Connacht, Leinster and inland Munster.
Snowy in the Cahir area of Co. Tipperary. All road users are asked to exercise caution and reduce speed. pic.twitter.com/V4BpX0KXLV
— An Garda Síochána (@GardaTraffic) January 31, 2019
In Wicklow, the Old Military Rd (R115) remains closed this evening between Glencree and Sally Gap due to icy conditions.
Sligo County Council said while conditions improved from yesterday, frozen snow and slush remained in many areas and motorists and other road users should continue to exercise caution, particularly on untreated local roads.
Gardaí in the midlands were warning road conditions were dangerous on many secondary routes and local roads, but there were no reports of any significant snowfalls.
As many as 20 schools that were closed yesterday in the Longford, Leitrim and Roscommon area were expected to reopen today.
Met Éireann was predicting snowfalls on higher ground this afternoon.
AA Roadwatch said road conditions were wet in Cork city, Waterford city and Tralee, while icy conditions were reported on secondary routes around Thurles and Letterkenny.
Meanwhile, Irish Rural Link, the national network representing the interest of rural communities, urged older people to keep safe and keep warm during the cold weather over the next few days.
It urged people to keep in contact with elderly neighbours to ensure they have enough fuel and food.
In the UK, the Met Office issued an amber warning for snow today, covering London and southeast England, the South West and Wales.
The warning follows the coldest night of the winter so far there with Braemar in Aberdeenshire the coldest spot as temperatures dipped to -11C.
Wind-chill temperatures in parts of the Northern Plains and Great Lakes plunged as low as -41C in Park Rapids, Minnesota, and to -35C in Fargo, North Dakota, according to the National Weather Service.