Cold conditions continued to grip the country today as temperatures stayed below freezing.
AA Roadwatch said many roads around the country remained hazardous, and called for drivers to take extreme care and slow down.
Bus Eireann provided a special Christmas Day service between the country's main towns and cities to help thousands of stranded passengers get home.
Dublin Airport is closed for the day and is expected to reopen early tomorrow.
All main routes were open but the Road Safety Authority (RSA) warned that while the big freeze will begin to ease in the next 24 hours, driving conditions will remain treacherous.
RSA chief executive Noel Brett pleaded with road-users to take extreme care.
"There is a danger that road-users, and particularly motorists, will be lulled into a false sense of security as conditions improve after the recent freezing conditions," he said.
"Roads right across the country will remain extremely dangerous, with lingering patches of snow and ice posing serious risks for all road-users."
Met Eireann also warned of a risk of localised flooding as snow and ice begins to melt and rain moves in from the west and south.
There is also a danger of further snowfalls and freezing rain over the next 24 hours.
The army said it would assist the health services by transporting healthcare professionals to medical facilities in Dublin, Cork, the Midlands and the west of the country.
The Defence Forces said its personnel would also help transport patients to Dublin from Cork and the Midlands for ongoing treatment, and a meals on wheels service is being provided to the elderly and housebound in locations around the country.
One of Northern Ireland's busiest roads was closed today because of collapsed overhead power lines.
Police shut a stretch of the M2 motorway between Antrim and Templepatrick on the northern outskirts of Belfast as electrical engineers repaired the damage, which they believe was linked to the extreme weather conditions.
With no immediate sign of a thaw and overnight temperatures as low as minus 15 degrees in some parts, gritters were out on most of the main roads.
Cold weather during the busy Christmas period has disrupted travel and business across Europe this week, and the prolonged period of severe weather is expected to clip economic growth in Germany, Europe's biggest economy.
Heavy snow stranded thousands of Christmas travellers in parts of Europe, with Belgium's main airport closed for most of the day to landing and icy roads in Sweden choked with traffic.
A spokesman for Brussels' airport said hundreds of beds were ready for stranded passengers after the airport reopened to inbound flights following a day of delays and cancellations.
In Sweden, heavy snowfall across southern parts of the country caused major traffic problems on roads and railways for the second day running yesterday.
The Swedish Transport Administration predicted tough weather conditions would disrupt travel today, with many trains likely to be cancelled.
About 2,000 people were forced to spend Thursday night at two main airports in Paris as snowfall in the north and east of the country continued to disrupt transport services..
Paris airports' authority chief Pierre Graff said de-icer producers were at the limit of what they could deliver. "There was a serious supply problem yesterday which we overcame with some incredible acrobatics," he told RTL radio.
The disruptions follow travel chaos earlier in the week, when tens of thousands were stranded across Europe as delays and cancellations of flights and high-speed trains were compounded by road travel restrictions.
Authorities throughout Europe warned of further disruptions in the next few days.
Heavy rain in northern Italy caused problems in some cities including Venice, where shoppers and tourists were forced to wade through knee high water in Saint Mark's square.
In Vicenza, to the west of Venice, there were fears that the Bacchiglione river could burst its banks and some residents were evacuated from their homes.
Britain's main air travel hubs had some cancellations and delays yesterday but London's Heathrow, the world's busiest international airport, said both of its runways were open.
Most main roads in England remained clear, but the Highways Agency warned motorists about the danger of icy roads as Britain headed for its coldest December in decades. Parts of Scotland and possibly northeast England were forecast to have a white Christmas.
Additional reporting: Reuters/PA