Icy conditions have severely affected roads in many parts of the country, with temperatures due to fall to -5C overnight.
Motorists have been urged to be extremely careful on the roads as the cold snap continues to make driving hazardous.
Bus Éireann says bad weather has disrupted and delayed its services from Limerick to Tralee, Killarney and Galway. Bus delays are also reported in the northeast.
Further icy conditions are forecast for tonight, with temperatures expected to dip to -5C and more snowfalls expected.
Disruption is likely to continue tomorrow, as hail, sleet or snow showers are expected in Connacht and Ulster, and parts of west Munster.
Today, the snow and ice caused hazardous driving conditions on thousands of kilometres of local roads.
Across the country roads are in a dangerous condition in particular where snow has fallen, but severe frost has also left many roads extremely dangerous.
Among the worst affected counties are Cavan, Roscommon, Donegal. In Co Wicklow, a number of cars were stranded as the Sally Gap became impassable.
Up to 15cm of snow was reported in parts of Longford and Leitrim.
Some school bus services did not operate today and as a result primary and secondary schools in many areas have closed.
The Road Safety Authority said that driving tests may be disrupted or cancelled for the rest of the week.
The Authority said candidates are advised to check www.drivingtest.ie for updates.
As well as school closures, many local events have been cancelled as the freeze continues.
Dublin, Cork and Shannon airports are experiencing some delays with passengers being advised to check in as normal and check their airline's website. (More information here.)
Air travel has been disrupted across Britain and mainland Europe with hundreds of flights delayed or cancelled.
Severe weather in England forced the closure of Gatwick Airport.
The airport’s runway was closed after 3pm ‘for essential de-icing work’, but reopened at around 8pm.
Passengers travelling from Gatwick are advised to allow extra time for their journey to the airport and contact their airline for the latest flight information.
Flights arriving at and departing from London Luton Airport are suspended. Passengers are advised to contact their airline.
Heathrow, Stansted and Manchester airports say some flights may be subject to delay as a result of the bad weather in the UK, mainland Europe and the US.
Meanwhile, Eurostar passenger services between Paris, London and Brussels have been suspended for a third day while further tests are carried out on its fleet of trains.