Freezing temperatures, snow showers and strong winds are making driving conditions hazardous in many parts.
AA Roadwatch is urging motorists to exercise extreme care with fallen trees on many routes and with further snow and ice expected throughout the day.
Emergency services are dealing with a string of road crashes on the M4 Dublin-Sligo Road as a result of the weather, and traffic is said to be extremely heavy as a result.
Dublin Airport is reporting some delays due to aircraft de-icing and delays at other airports.
While disruption to passangers remains minimal, Dublin Airport Authority advised those intending to travel to consult airline websites before setting out.
Irish Ferries has cancelled its Swift sailings due to the extreme weather, but passengers are being accommodated on its cruise ferry.
Stena has also cancelled its 9am Rosslare to Fishguard service.
Temperatures fell to as low as minus 4 degrees last night.
Extreme cold, wind and snow will combine to make for some of the most severe weather so far this year, Met Éireann said.
It said tonight would be even colder with air temperatures falling as low as minus 6 degrees.
Met Éireann has issued a “status yellow” warning, the third most serious warning it can give under a new alert system.
However, it said tomorrow would be sunnier, dry and a little warmer but tomorrow night would again be extremely cold with frost and dangerous driving conditions likely overnight.