AA Roadwatch has said that road conditions have deteriorated across the country as compacted snow is refreezing.
Roads remain dangerous in many parts, particularly in the northwest, the west and the midlands, as well as west Cork.
There are long delays in Dublin, particularly in the south and west of the city and around suburban shopping centres.
Public transport companies are running services but snow and ice are causing delays and curtailments.
The Luas Red and Green lines in Dublin are running to schedule.
Met Éireann says with the exception of Leinster, most of the country will remain dry between now and Christmas Day.
It will be extremely cold again tonight with lowest temperatures of between -6C and -12C.
However, a change in the weather on St Stephen's Day will bring a different kind of severe weather and the possibility of flooding.
The Severe Weather Committee has said it is confident it will have enough salt supplies to keep the national primary routes open in the lead up to Christmas.
The statement came after a shipment of 3,000 tonnes of salt arrived in Dublin Port last night.
Sean O'Neill from the National Roads Authority said more salt is due in Cork tonight and further shipments should arrive over the next few days.
However, the Irish Road Haulage Association has said that not enough is being done to keep the roads clear.
The Irish Farmers' Association called for more co-ordination between State agencies and communities.
Airports working to clear backlog of flights
Aer Lingus and Ryanair say they are operating at close to normal capacity on short and long haul routes out of Dublin Airport.
Both airlines say their priority remains getting people home for Christmas, as many thousands of passengers whose flights were cancelled are being rebooked onto services.
Aer Lingus added capacity to UK routes with assistance from Aer Arann. Extra aircraft were also leased to clear routes into the US and eastern Europe.
Ryanair says its fleet of over 200 planes were almost all in operation and it experienced only minor restrictions at UK airports.
The airline has also announced that it is adding 14 extra flights to its Belgium, France, Ireland, Poland and UK networks tomorrow to allow disrupted passengers return home for Christmas.
The Dublin Airport Authority says much of the backlog should be cleared in the next 24 hours if the weather remains clear.
Cork, Knock and both Belfast airports are open, but delays are expected because of problems at other airports.
Elsewhere, many European airports have been clearing a huge backlog of passengers stranded over the past week by snow and ice.
Meanwhile, the HSE has warned that ambulance journey times are worsening because of the state of by-roads particularly in rural areas.
Spokesman Gavin Maguire said people will have to understand that ambulances are for emergency use and he said journey times are getting longer.
An Post says deliveries are slower than normal and that staff will be working long and late to get Christmas cards and presents to their destinations this week.
Problems have been reported with collections in west Cork and Wexford because of snow falls yesterday.