Temperatures have fallen to -4C degrees in the West tonight and driving conditions remain difficult.
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Gardaí say it is clear that many people have heeded warnings not to travel unless journeys are absolutely necessary.
They say the volume of traffic on roads across the region is considerably less than it would normally be and there have been surprisingly few accidents.
Many meetings and social events in counties Galway and Mayo have been cancelled.
All main roads in Galway and Mayo have been gritted but gardaí in Clifden say minor roads in Connemara - particularly in the Inagh Valley - are still very dangerous.
In Ballinasloe, traffic is moving well on the M4 motorway and other main roads but here too by roads are in a dangerous condition.
Gardaí in Gort say roads there have been gritted recently are safe to drive on - with care.
In Claremorris and Castlebar in Co Mayo, compacted snow and patches of black ice are creating hazards on many less used back roads.
One of the biggest problems to emerge during the day has been the large number of houses which now have frozen water pipes.
Hundreds of homes in the Turloughmore/Abbeyknockmoy area of Co Galway are without water. Farmers say the situation will become critical within the next few days if temperatures drop any further.
Drivers are once more being urged to use public transport and to avoid driving if possible.
Hundreds of schools remained closed for a second day, but there has been only limited disruption to public transport. Get information on school closures here
As the cold weather continues, Met Éireann is warning that overnight ice may pose difficulties for motorists across the country.
Further snow falls are expected, particularly in Leinster and parts of Munster.
Met Éireann says temperatures will fall again tomorrow and Thursday.
Roads in Westmeath are especially hazardous tonight with motorists strongly advised not to travel unless absolutely necessary.
In the east, south Dublin and higher ground in Wicklow are badly affected. There were long tailbacks southbound on the M50 and N11 this evening.
Most of the main routes in Co Cork have been treated. However, secondary and local roads continue to remain hazardous in parts, especially on high ground.
Elsewhere most commuter services are running largely to schedule.
