Met Éireann's snow-and-ice weather warning remains in place as more snow is forecast in some parts today.
Cavan, Monaghan, Donegal, Louth, Dublin, Kildare, Wicklow and Meath will be affected, although accumulations will be small.
In the North however, heavy snowfall has forced the closure of many roads and more than 14,000 homes are still without power.
Emergency repair crews worked into the night to restore power to thousands of homes.
Northern Ireland Electricity (NIE) said the weather was improving but snow was still blocking roads.
Northern Ireland Water said about 500 homes still had problems with their water supply in south Antrim and west Belfast.
Julia Carson, NIE communications manager, said: “The weather does seem to be improving, wind speeds have dropped, but due to the extent of the damage across northern and eastern counties it may be a few days before customers are back on supply.
“Some roads are still impassable, access has also been restricted because of drifting snow, and abandoned vehicles, they’re also causing access problems for us.”
The situation has improved for many since yesterday morning, when 35,000 electricity customers were cut off and up to 1,000 homes were without water.