Met Éireann has issued a severe weather warning and said more snow and freezing temperatures are expected overnight.
Sub-zero temperatures and snow falls today resulted in widespread disruption to road and air traffic.
Gardaí have warned motorists to take extreme care.
Flights at Dublin airport were seriously disrupted after the runway was temporarily closed to allow snow to be cleared. It was later reopened.
Dozens of Aer Lingus and Ryanair flights had to be cancelled and some inbound flights were diverted.
Delays are still being experienced at the airport and both airlines are advising prospective passengers to check if their flights have been cancelled before travelling.
It is expected the cold snap will result in further disruptions to transport tonight and in the morning.
Gardaí warned motorists to expect serious delays city wide due to adverse weather conditions.
There were serious tailbacks on the N7, N4 and M50, and heavy vehicles reported difficutlies.
Gardaí urged anyone who intended to travel to consider alternative arrangements, and motorists were asked only to travel if it was absolutely necessary.
There were a number of minor accidents around the country, including four on one stretch in Sligo.
The worst of the weather affected Leinster and east munster with some parts of Donegal also affected. Schools in Carlow, Kilkenny as well as Meath were shut allowing students to practice some unusual sports.
Unsurprisingly, the weather also badly disrupted transport services along the east coast.
Aer Lingus had to cancel all flights to Heathrow from Dublin, Cork and Belfast. Ryanair also had to cancel some flights.
Bus Éireann services were also hit.
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Met Éireann is forecasting more snow over the next 24 hours with temperatures falling to -3C tonight.
Road surfaces are very treacherous in parts of the midlands and east Leinster, particularly in Wicklow, Kildare and Laois.
While the blanket of snow which covered many parts of the country made for some picturesque scenes this morning, the morning commute to work was hazardous for many.
Gardaí have advised motorists to exercise extreme caution, particularly in the southeast counties were some rural roads are described as treacherous.
Some Bus Éireann services are also disrupted with passengers advised to contact their local travel centres for advice.
Air passengers are also facing long delays, with flights out of Dublin, Cork and Belfast affected by the severe weather.
Britain has been particularly hard-hit by the freezing conditions, with all airports experiencing some disruption. This has had knock-on effects at Irish airports.
London's Gatwick and Heathrow airports were two of the worst affected - they have now reopened and are dealing with a backlog of flights.
Passengers travelling by plane from Ireland to Britain are asked to contact their airline or to check their flights online.
There is also disruption to Commuter and Intercity services on the Dublin to Rosslare line following a rock fall between Bray and Greysones.
Gorey commuter services and Rosslare Intercity services are being part substituted by buses.