‘Treacherous conditions’ have been reported on some roads as heavy snow fell in parts of the south and west of the country overnight.
A Status Orange warning for snow and ice is in effect for counties Clare, Limerick, Tipperary and Galway, while an Orange warning for snow and rain is in place for counties Cork and Waterford.
Both Status Orange warnings are in place until noon.
Elsewhere, a Status Yellow low temperature and ice warning for the entire country is in place until midday, while a Yellow snow and ice warning, which came into effect yesterday evening for 14 counties, has been extended to include Dublin, Mayo, Roscommon, Longford and Westmeath.
In Northern Ireland, a Yellow ice warning for counties Antrim, Armagh, Down, Fermanagh, Tyrone and Derry is in operation until 10am.
In Co Mayo, gardaí reported treacherous conditions on the roads, especially between Castlebar and Westport and on the N5.
A number of trees are down due to heavy snowfall.
Heavy snow was also reported in Galway overnight, with travel on rural roads said to be difficult.
A number of incidents have been reported on the M6 motorway, with a single vehicle collision near Junction 14 on the westbound carriageway between Loughrea and Athenry.
Another collision between the Ballinasloe exits on the motorway is also causing delays and some roads around Conamara are impassable.
A diversion is in place between Moycullen and Oughterard after a truck jackknifed, blocking the N59.
The volume of snow has complicated efforts by local authority crews to clear and grit routes overnight and this morning.
There have been reports of a number of minor collisions involving cars and busses around Galway city this morning also.
In Limerick, there have been snowfalls around Newcastle West, Adare and Patrickswell, making road conditions challenging.
Snow also fell in parts of Co Clare, including Miltown Malbay, Doonbeg and Kilkee.
Gardaí in Ennis said there was some snow but it is not sticking, with similar conditions reported in north Tipperary.
There has been more rain than snow in Co Cork, with an estimated 20mm of rain falling since midnight.
There are some reports this morning of sleet in the north of the county around Mallow, but there are no reports of any incidents on the county’s roads so far.
Local gardaí say there is pooling of rainwater on some primary and secondary roads and motorists should continue to exercise caution.
Cork County Council crews, who have been busy gritting and salting Priority 1 and 2 routes since Tuesday, remain on standby.
There has been no disruption to flights to and from Cork Airport this morning, with trains also currently operating as scheduled.
Some schools have decided to open late this morning as a precaution.
Bus Éireann said a number of its services today have been disrupted due to the weather.
The 6.05am and 7.05am 336 buses from Doonbeg have been cancelled, as has the 7.20am 333 route from Kilkee, the 05.30am 450 Westport to Achill service and the 7.10am Achill to Westport service.
Iarnród Éireann said all of its trains are currently operating on schedule.
Road users are being advised to avoid making unnecessary trips in affected areas while Status Orange warnings are in effect.
The Road Safety Authority (RSA) said road users can expect very difficult travelling conditions and poor visibility.
For pedestrians, the RSA advised that the cold spell will lead to difficult conditions underfoot and flooding is possible, and that slips and fall accidents during winter can cause serious injuries.
Cyclists are being warned to wear high-visibility clothing and ensure their bike lights are working correctly.
Salt and grit supplies have been checked and replenished across the county with gritting trucks ready for deployment when required.
Waterford City and County Council has activated its severe weather plan and authorities are urging the public to exercise caution.
The council warned that Priority 3 roads would only be treated when resources allow and during normal working hours.
There have been no problems reported in the county so far this morning.
Extra bed capacity for any known rough sleepers was made available by Waterford City and County Council ahead of the weather warning.
The local authority said beds will be available at McGwire House on Bath Street, while women and children seeking refuge from domestic violence should present to Oasis House on Morrison’s Road in the city.
It also appealed to the public to contact the homeless services team if they see people sleeping rough in the city.
In Dublin, the CEO of the charity Dublin Simon described the current cold snap as “an emergency” that requires “an immediate response”.