Met Éireann has issued two new snow and ice warnings as the national forecaster also warns of some thunderstorms and "blizzard conditions".
An orange alert, the second highest warning, is in effect until 6pm on Friday.
Heavy showers of hail, sleet and snow are expected to hit Ulster and Connacht.
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The alert warned there is a “risk of drifting and blizzard conditions” and scattered thunderstorms during the two days.
There is a yellow weather warning for snow and ice in Leinster, Munster and counties Galway and Roscommon from Thursday at 5am until 6pm on Friday.
Snow is expected to build-up on low ground but particularly on higher levels.
Meteorologist Matthew Martin said Thursday would be a “bitterly cold” day.
“The temperatures themselves won’t be anything spectacular, probably a maximum of 2 or 3 degrees, but it will sub-zero because there is going to be very strong north westerly wind,” he said.
“The worst of the conditions are going to begin to arrive in the north to west later tonight and into tomorrow morning.”
Mr Martin told The Irish Times the heaviest snowfall would be in Ulster and north Connacht of between 2cm-5cm and probably more in higher grounds.
“Particularly tomorrow evening and early tomorrow night would be the best chance snow of settling elsewhere across the country,” he said.
“From 6am tomorrow morning the showers are likely to fall sleet and snow countrywide.”
Mr Martin said along the Atlantic and north coasts there was a risk of thunderstorms and lightning within the heavy showers.
The term “thundersnow” has been used online to describe a thunderstorm with snow mainly falling instead of rain.
However, Mr Martin said it was not a meteorological term.
“The heaviest of the snow fall is most likely over Ulster, Connacht, north Leinster and west Munster and especially so on high ground,” Met Éireann said.
Road users
Gardaí have asked road users to be careful when travelling over the next few days during the bad weather.
They have advised drivers to slow down as visibility might be reduced, use dipped headlights, manoeuvre gently and leave extra distance between vehicles.
On Wednesday morning, strong winds knocked several trees across the country causing traffic delays.
AA Roadwatch said trees had fallen on roads in counties Wicklow, Wexford, Waterford, Offaly and Donegal.
It has also warned drivers wind-blown debris is likely to be on secondary routes and said high-sided vehicles were particularly vulnerable to wind gusts on exposed roads.
Scattered showers on Atlantic coasts were expected move inland overnight on Wednesday and turn “increasingly wintry”, with snow on high ground, the meteorological service said.
Temperatures were likely to reach lows of minus 1-2 degrees.
Thursday will also be a very cold day, with the risk of sleety rain and snow affecting the far south of the country for a time.
It will be brighter elsewhere with wintry showers of hail, sleet and snow, mostly across Connacht and Ulster.
Wintry showers will continue in the west and north through Thursday night, with widespread frost and ice.
An emergency meeting of the National Emergency Co-ordination Group, which includes Government departments and key bodies such as Met Éireann and the gardaí, was held on Wednesday in advance of the cold weather.
In a statement, the group said Transport Infrastructure Ireland would be salting national routes and motorways and clearing snow where necessary.
The group asked the public to “call on elderly relatives and neighbours, and offer to assist them” during the coming severe weather.
It also asked the public to ensure they have sufficient food, medication and fuel supplies.
‘Winter ready’
Minister for Transport Shane Ross asked people to be "winter ready" and to take all necessary precautions ahead of the cold snap.
“I would urge all people to heed the advice of the agencies and take all necessary precautions if out during the severe weather.
“If travelling I would advise that you plan your route and check local information, allow extra time, drive slowly and carefully and stay safe,” Mr Ross said.
Further information on how to prepare for severe weather is available at winterready.ie.
The Department of Transport also publishes transport information for severe weather here.
As of January 2nd, salt usage to date this winter amounted to 38,400 tonnes, with stocks of 203,500 tonnes remaining.
The department said this compared with 96,000 tonnes of salt used over the winter of 2015/16 and some 130,000 tonnes used during the very severe winter of 2010/2011.
Transport Infrastructure Ireland provides details of motorway and national road conditions on tii.ie and tiitraffic.ie.
Local authorities will also publicise local roads closures, and a number of local authorities provide mobile alert services which include updates on any such closures, Mr Ross said.
Information on traffic and road closures can also be found on the AA Roadwatch website, theaa.ie/roadwatch, and on local radio stations.
The Road Safety Authority provides information and safety advice for drivers, motorcyclists, cyclists and pedestrians at rsa.ie.
Central and east-southeastern Europe have in recent days been gripped by a mid-winter deep freeze and snowstorms.
With temperatures dropping below -30 Celsius, at least 25 people died over the weekend, mainly in Poland.
