The ESB is working towards restoring power to the majority of impacted customers by tonight, but says the damage in South Kerry and West Cork is so extensive, that they may be without power overnight.
There are pockets of outages across Longford and Leitrim.
A nationwide yellow wind and rain warning is in place until 6pm, while a yellow snow and ice warning is in effect for the whole country until 10am tomorrow.
Chair of the National Emergency Co-ordination Group, Keith Leonard, is urging people to delay journeys in severely impacted areas.