Met Éireann has warned that the southwest of the country will bear the brunt of the freezing weather conditions tonight with heavy snowfalls expected.
Gardaí say many roads around the country are in a dangerous condition and have urged motorists to only travel if absolutely necessary.
The northwest, west and the midlands are worst affected with many national primary routes reported to be very icy.
Met Éireann has said it will be extremely cold tonight with patches of freezing fog. There will be some snow showers in Connacht, west Munster and along coasts of north Leinster, with temperatures between -4C and -10C.
AA Roadwatch says that roads are freezing hard and extreme care should be taken on all routes. Roads throughout Munster are hazardous, and in Connacht routes around Galway city are very icy.
Limerick City Council says the main roads into the city have been gritted.
Clare County Council has delivered grit to 48 locations throughout east and west Clare to be used by local communities on public roads in their localities, which have not been gritted by the council itself.
Communities are being advised to prioritise hilly sections of their neighbourhoods, and not to use the grit for their own driveways.
Bus services between Cork and Limerick were affected by the snow early this morning but have since resumed.
Bus Éireann says services in Kerry have also resumed.
Some services from Dublin to Letterkenny and Derry were cancelled.
Irish Rail had a full service today on all Intercity, DART and commuter routes. Dublin Bus also had a full service.
In the northwest and midlands, the Defence Forces transported healthcare workers in Mullingar, Athlone, Galway, Moate, Castletown-Geoghegan, Castlepollard, Boyle, Banagher and Monaghan.
Troops were also deployed on snow clearance operations in Donegal Town, Ballyshannon, Ballybofey, Letterkenny and Buncrana.
Northern Ireland is also experiencing severe weather conditions.
There is a deep blanket of snow covering most parts but an emergency flash warning for extremely heavy snow in counties Antrim, Down and Derry has been lifted.
A Roads Service spokesman said motorists should be aware that driving conditions remain very hazardous, and that they should exercise extreme caution on all roads.
Airports hit by severe weather
Air travellers are advised to contact their airline before setting out.
Dublin Airport is fully operational, but there are some delays and cancellations due to adverse weather conditions at other European airports.
Cork and Shannon airports are also fully operational, as is Ireland West Airport Knock.
Belfast International Airport, which was closed yesterday, is open today but some delays and cancellations can be expected.
The runway at City of Derry Airport has reopened and operations have resumed but delays and restrictions are expected.
Flights in other European countries have also been affected.
All Aer Lingus flights for the rest of the day into and out of Gatwick and Heathrow airports are cancelled due to the severe weather in the London area.
Customers are asked to view the website to make changes online or request a refund.
Ryanair says that due to heavy snow in France, Germany, Northern Italy and Ireland, flights are subject to delay and possible cancellation.
Pisa and Venice Treviso Airports in Italy are both closed due to snow.
BA has cancelled all of its flights from London Heathrow, which were due to depart between 10am and 5pm today.
All BA European and domestic flights from London Gatwick between 10am and 4.59pm have also been cancelled.
Southwest at significant risk of snowfalls
Speaking at a press briefing following a meeting of the Government's emergency taskforce, meteorologist Gerald Fleming said the worst affected areas overnight were the northwest and the southwest, although some areas escaped.
Mr Fleming said tomorrow night the risk would move to the southeast of the country, where counties like Waterford, Wexford, Kilkenny and Wicklow could see snowfalls.
He said the weather will get progressively colder over the following 3-5 days, but will be drier, with just some snow showers.
He said it now looks likely that there will be a significant thaw between 24 and 27 December, but said that is too far away to be definitive.
Motorists urged to drive with care
Also speaking at the briefing, Insp John Ferris of the Garda Press Office appealed to road users to exercise continuing care.
He said the nature of the weather was such that conditions varied from mile to mile and so drivers need to remain on their guard at all times, plan journeys and drive slowly.
He particularly appealed to pedestrians to take care, and asked people not to walk home alone in the bad weather.
Committee chairman Sean Hogan again appealed to members of the public to clear snow before it compacts.
In doing so, he said, it would remove the hazard ahead of an important and busy week.
Joe Crockett, chairman of the major emergency group of local authorities, said very significant local authority resources had been deployed, particularly in the northwest and southwest.
In Mayo, 17 gritters were on the roads overnight. He said the arrangements in place with the National Roads Authority regarding the supply of salt were working well.
He said local authorities financial resources were being stretched by the continuing bad weather but the recent extra allocation from central Government had helped, however it was too early to put a figure on the cost of the cold spell.
Dublin City Council said it would continue restricting water supplies overnight to conserve stocks.
Michael Phillips from the council said water in city centre areas would not be shut off until 10pm tonight to facilitate bars and restaurants, but from tomorrow it would revert to a 7pm to 7am shutoff period.
He said demand had stabilised and the council continues to hope to revert to normal supplies between 23 and 28 December.
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