More than 18,000 homes and businesses are without power according to Northern Ireland Electricity (NIE), who said it had some 600 staff working to reconnect the customers.
Large areas of counties Tyrone, Londonderry and Antrim were lashed by blizzards, heavy rain and high winds on Tuesday, with up to 300 people rescued from a mountain road after conditions overwhelmed vehicles.
NIE hopes to restore power to a significant number of customers tonight but there will be many left without supply tomorrow in the areas worst affected by the ice storm.
Parts of North Antrim have been particularly hard hit but the company said it was hoping to restore power to the majority of affected homes by Friday.
In Cloughmills, NIE engineers are rebuilding 4.5 miles of electricity lines which were brought down and damaged, including replacing 60 electricity poles.
It said the work would normally take a number of weeks, but is being done in a matter of days and hours.
Sara McClintock of Northern Ireland Electricity said: “We will continue with all of our efforts to restore all of our customers as soon as is humanly possible. We hope that more accurate estimates of restoration times for individual faults will continue to become available throughout the evening.”
Energy Minister Arlene Foster said: “In the space of several hours on Tuesday evening we were faced with unprecedented weather conditions which caused extensive damage to the electricity network in Northern Ireland.
“I want to reassure those who are without power that my Department has been liaising with NIE to ensure that all possible action is being taken regarding the restoration of power and the safety of customers.
“Whilst I pay tribute to all NIE workers who are working night and day in dangerous circumstances, I also recognise that many of our most vulnerable citizens are sitting without heat or light. I have personally asked management at NIE to ensure every effort is made to have power restored to all domestic and business customers as soon as possible.”
Meanwhile, police in the North have revealed they had to rescue a family who were snowed-in to their home.
Police had to go to the aid of a family in the Plumbridge area of Tyrone who were running out of food and fuel in their snowed-in house today.
Sergeant Stephen Creighton of police search and rescue said: “Once the situation was reviewed I contacted north west mountain rescue who sent out three Land Rovers to try and reach the family.
“Unfortunately the heavy snowfall made any attempts by the volunteers to get close to the house impossible.
“Our main concern was the young children in the house who would not have been able to make it through the snow which was 8ft deep in places.
“The adults were able to make it to the Land Rovers, However we used the police helicopter to transfer the children from the house to their parents.” More than 100,000 homes and businesses suffered power cuts due to the weather and it could take days before all customers have supply restored.
Police, coastguard, mountain rescue crews from Northern Ireland and the Irish Republic, plus Department of Environment roads service staff launched a joint rescue operation on Tuesday night after motorists became stranded when snowdrifts swept across the mountainous Glenshane Pass, a main route between Belfast and Derry.
PA