Temperatures of minus seven degrees overnight will lead to extremely dangerous driving conditions through the night and tomorrow morning.
Although light snow and sleet is predicted for the next 24 hours, the main dangers for drivers will be caused by frost, ice and compacted snow.
Dublin Airport says there are still some delays following yesterday's closure.
The Stena Line HSSis out of service until further notice due to storm damage. There will be no sailings between Dun Laoghaire and Holyhead. Those wishing to travel should go to Dublin Port where Irish Ferries are operating as normal.
There is disruption to the Stena Line sailing from Rosslare. Passengers intending to travel on the 22:15 sailing tonight should contact 01-2047777.
Meanwhile some households in Northern Ireland and the Republic will be without power for a third consecutive night as repair services have not reached all homes affected by the Monday night's bad weather.