About 7,000 homes and businesses are without power after storm-force winds battered the country.
The ESB said network crews will be out restoring supplies, particularly in Donegal where 5,000 customers have no electricity.
At the height of the storm overnight up to 25,000 customers were without power as strong winds, falling trees and debris damaged power lines.
A weather warning remains in place for Donegal, Galway, Leitrim, Mayo and Sligo, where gusts will reach up to 110kph (68mph).
AA Roadwatch warned motorists to drive with care following heavy snow in parts of Sligo, Tipperary, Offaly and Laois.
The promenade in Salthill also remains closed because of flooding.
Yesterday, a 23-year-old woman died after a tree fell on her car in Mullingar, Co Westmeath.
Kent Train Station in Cork city has reopened after a canopy covering two platforms was blown off in strong winds yesterday, injuring three customers.
The wild weather will continue to batter Ireland and the UK as thousands of people recover from flooding and power disruption to their homes brought on by heavy downpours and gale-force winds.
Gusts of up to 145kph (90mph) are expected to cut across Northern Ireland and parts of western Scotland, while there are warnings of up to 20cm (8in) of snow in Scotland and icy roads across much of England.
Storms caused by an Atlantic depression left 7,000 customers without electricity in Northern Ireland last night, though most have now been reconnected, with another 3,500 affected in north-west England and almost 900 in South Wales.
Northern Ireland Electricity (NIE) said last night that it expected further damage to the electricity network as bad weather is set to continue.
Some 1,000 customers were without electricity as of 11pm because of trees down across power lines and broken electricity poles, though NIE expected the number to rise during the night.
Spokeswoman Julia Carson said: "We were prepared for the storm and have already restored over 6,000 customers to power since the winds swept across Northern Ireland this afternoon.
"However, we are expecting the winds to peak in the early hours of the morning, causing additional disruption to electricity supplies, especially in eastern and northern areas."
Northern Ireland Electricity said it had restored electricity supplies to around 10,000 customers. Just 70 remain without supply with engineers and emergency crews responding to faults in Co Down and Co Antrim.
Julia Carson, NIE communications manager, said: "We may need to take some customers off supply this morning to facilitate permanent network repairs but we hope to have electricity restored to the majority of homes by lunchtime."