The freeze will continue until Friday at least, and AA Roadwatch has warned that driving conditions are likely be "twice as bad" as yesterday in many areas.
Motorists should not make any journey unless "absolutely necessary" where ground conditions continue to be bad.
As up to four inches of snow fell across the State yesterday, 7,000 households in the east and north were still without power this morning. More than 1,000 ESB technicians, who restored power to up to 40,000 customers yesterday in Donegal, Mayo, Louth, Dublin, Kildare, Carlow and Wicklow, will begin restoring power to the remaining households today.
Those areas still without power this morning are the Omeath and Cooley peninsula in Co Louth, rural areas around Drogheda and Dundalk, north Co Dublin and rural Co Wicklow. All will have electricity by this evening, Mr Michael Kelly, an ESB spokesman, said.
Mr Kelly described the conditions in which the technicians have been working as "horrendous".
Power cuts were caused by trees falling on lines, high winds and the weight of the snow in places. In the north-east some poles were so heavily iced that technicians could not climb them and supervisors had to abandon attempts at repair until conditions improved. In Louth and Co Dublin ESB technicians were unable to reach many power lines and poles where roads were also impassable.
Up to four inches of snow fell across the north, west and east of the State yesterday, with winds gusting up to 40 m.p.h., considerably reducing air temperatures to about 10 degrees lower than the seasonal norm of 9 to 10.5 degrees.
Although the "worst of it is over", Mr Gerald Fleming of Met Eireann said conditions would continue hazardous and very cold, with a full thaw not expected until the weekend.
"These conditions came after a weekend which felt quite pleasant, with light winds. There we had high pressure which for a while had given us warm weather. This current weather system which came on Monday is now stagnating over Britain, and we have an arm of it over the east.
"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." He said conditions were not expected to improve quickly and the combination of low temperatures and continued precipitation would make for "very frosty, very nasty conditions for both walkers and motorists".
AA Roadwatch has warned motorists that, although snow may not be falling in the same volume today and tomorrow, the already fallen snow will have frozen overnight, making driving conditions "twice as bad" as yesterday.
"We are asking motorists not to travel unless they absolutely have to," said Ms Evanna Lyons.
Bus Eireann cancelled its 14 services between Belfast and Dublin. Passengers faced long delays on most routes, especially the Naas-Dublin route where journeys were taking over two hours. The journey in normal conditions was less than an hour, a spokesman for the company said.
Mr Cyril McIntyre of Bus Eireann said all services would set off on schedule this morning, but he advised intending passengers to contact their local stations for updated information.
