Up to five centimetres of snow may fall in some parts of the country this evening with the cold snap expected to last until at least the middle of the week.
A band of snow showers crossed the country this morning making driving conditions hazardous, particularly in the south. Sleet, snow and black ice were reported in counties Kerry, Cork, Westmeath, Limerick, Tipperary, Roscommon and Sligo.
Up to four inches of snow fell in parts of Donegal and roads were, in some cases, impassable. AA Roadwatch warned that road temperatures had fallen below zero.
Conditions were wet and windy in many parts of the north-west and west and there are sleet and snow showers in the south, the east and in the midlands.
Driving conditions on the N20 from Newcastle West to Limerick city were dangerous due to snowfall and snow also affected driving conditions on the N6 between Ballinasloe and Loughrea in Co Galway.
Gardaí in Wicklow advised motorists to avoid the Sally Gap due to icy conditions, and in Donegal the N15 at the Barnesmore Gap was passable, but with care.
Roads were very wet in Dublin this morning, and traffic was also heavier than in recent weeks, AA Roadwatch said.
Temperatures fell throughout the day and a further band of showers moving in from the Atlantic this evening and tonight will lead to snowfall of between 2 to 5 centimetres with high ground most at risk, according to Met Éireann. While it will not be as cold as it was before Christmas, there is a greater risk of snow falling due to wetter conditions.
"This very cold and often windy spell will continue up to mid-week at least. Most areas can expect falls of sleet or snow at times, leading to some accumulations. The nights will be frosty in most places also, with some icy roads," the meteorological service said in its latest weather warning.
The cold snap will continue until Wednesday when there will be a brief respite before temperatures drop again on Thursday.
Storms battered the country on Saturday and led to the death of a 35-year-old woman in Co Down. A tree fell on her car on the Strangford Road in Downpatrick at about 4pm.
The weather caused extensive damage to eircom's network across the country over the weekend with damage to overhead wires caused by falling trees as well as a large number of fallen and damaged telephone poles. The wost affected areas include parts of Mayo and the western seaboard, Louth, South Kilkenny and Waterford.
There are currently up to 7,300 telephone faults on the company's network. In a statement the company said crews were working to restore services to customers as quickly as possible.
Weather conditions also caused the loss of electricity in 90,000 homes in the Republic and more than 40,000 homes in Northern Ireland. ESB and Northern Ireland Electricity crews worked through the weekend and expected to have the vast majority of homes reconnected by late last night.
An ESB spokesman said the work was hampered by lightning storms along the west coast.