Widespread disruption is expected today after the country was brought to a standstill this week
A status red snow-ice warning has been lifted, after two days that saw the country effectively shut down.
Some public transport services have begun operating again, but widespread disruption is expected due to the heavy snow in recent days.
Met Éireann has downgraded the weather warning to a status orange for Munster, Leinster, Cavan and Monaghan, saying there will be "widespread treacherous surfaces" due to ice and lying snow.
The snow is also set to start melting, bringing a risk of flooding in some parts.
A lower-level status yellow snow-ice warning remains in place for Connacht and Donegal.
Speaking after a meeting of the National Emergency Coordination Group this morning, Taoiseach Leo Varadkar said: "While things are slowly improving, we don't wish to lull people into a false sense of security.
"There may be more snow today, and road surfaces are treacherous in many areas due to ice and lying snow. I directed that all resources of the State work to get Ireland back-up-and-running and moving safely again."
Around 20,000 homes & businesses remain without power, and Leo Varadkar says it is hoped all faults will be repaired within 36 hours.
I’m informed that our troops are currently clearing snow and ice to make sure patients, staff and visitors can access Crumlin Children’s Hospital. @defenceforces and @CivilDefenceIRL are working closely with HSE. @SimonHarrisTD @campaignforleo— Paul Kehoe T.D (@campaign4kehoe) March 3, 2018
The motorway system is open despite 'challenging conditions', and local authorities - aided by members of the Defence Forces - are working to clear roads.
Irish Rail services began to operate again earlier this afternoon.
However, there is significant disruption - with Dublin Heuston services not resuming until at least 5pm this evening, and DART services temporarily not running between Dun Laoghaire and Grand Canal Dock due to flooding.
Dublin Bus has confirmed buses are on the roads this afternoon, but notes: "Services will operate on main roads only, will have reduced frequencies and there will be diversions in place."
Bus Éireann services have begun operating again in parts of the country, with a full timetable available on their website.
The Luas Red Line is now operating between The Point and Red Cow, following an earlier delay to services recommencing.
Transdev says trams will run every 30 minutes.
The Luas operators say there is no service from Red Cow to Tallaght, or from the Red Cow to Saggart.
The Green Line is not in operation today.
Dublin Airport, meanwhile, has reopened after all flights were grounded yesterday.
Shannon Airport reopened this morning, while Cork Airport has also now reopened for afternoon & evening flights after being closed this morning.
Ryanair and Aer Lingus have cancelled some early morning flights, and passengers are advised to check their websites for full details.
We're open, first flight landed at 5am. Please check with your airline re status of your flight BEFORE coming to airport. Taxis operating. @Aircoach operating to city centre, see its feed re other routes. @dublinbusnews resuming at noon. Campus roads are clear. #StomEmma #Snow pic.twitter.com/jfZI6sfHNV— Dublin Airport (@DublinAirport) March 3, 2018