Motorists are being advised that freezing temperatures could cause dangerous driving conditions in places.
Temperatures are forecast to dip to -5C in some areas overnight.
Met Éireann says a widespread severe frost will form with icy patches.
Poor weather conditions disrupted some road, sea and air transport today.
A few flights were cancelled at Dublin Airport due to adverse conditions.
A spokesperson said a number of flights had been diverted, and others were experiencing some delays.
Irish Ferries cancelled its Swift sailings due to the conditions, but passengers were to be accommodated on its cruise ferry.
Stena also cancelled its 9am Rosslare to Fishguard service.
Gardaí earlier dealt with several crashes on the M4 Dublin to Sligo road between Enfield and Leixlip.