AA Roadwatch has warned motorists not to undertake any journeys today unless "absolutely necessary" in areas badly affectedby the freezing weather.
There were no major snowfalls overnight but with a freeze setting in AA warned driving conditions are likely be "twice as bad" as yesterday in many areas.
According to Met Éireann the freeze will continue until Friday at least. It said up to four inches of snow fellyesterday.
Mr Ger Fleming of Met Éireann said: "We expect now that the worst in terms of snowfall is over but showers will be generated over the sea and blown in over the coast. So we can expect quite a few showers of hail and sleet over the next few days."
Dublin Airport has now reopened after its closure yesterday.
Dublin Bus, Bus Éireann and the DART service will operate as normal today. A section of the DART line between Howth and Howth Junction that was closed yesterday is expected to reopen this morning and all mainline train services will run normally. The Greystones to Arklow line is still closed due to flooding and fallen trees on the line. Bus transfers are in place.
Ferry services have also been hit. The Irish Ferries fast ferry will sail at 11.15 a.m. and has been moved forward an hour to accomadate the extra traffic from the cancelled 9.45 a.m. Inis Mór sailing, which will now sail at 12.45 p.m. approximately. The 9.30 a.m. sailing from Rosslare to Pembroke has been cancelled.
Up to 12,000 households in the north and east are still without power this morning as ESB workers continue their task of restoring power around the State.
Up to 40,000 people were affected by power cuts yesterday as high winds knocked trees onto lines and snow damaged them.
The worst affected areas were Donegal, Kildare, Carlow, Wicklow, Mayo, Louth and north county Dublin.
In the north of Ireland 70,000 homes lost power over gale-force winds.