Temperatures are expected to fall to as low as minus 6 degrees tonight with Met Éireann predicting a widespread severe frost.
The forecaster said it would be a cold and clear night with temperatures expected to drop to between -3 to -6 degrees.
It said the freezing temperatures would continue into tomorrow, with the risk of freezing fog in some parts.
The Road Safety Authority (RSA) has appealed to motorists to drive with extra care as ice was reported on several midland roads.
The RSA's Noel Brett urged drivers to be cautious, saying the cold snap "may catch people off guard after the very mild winter".
"I would ask each and every road user to slow down and in particular be aware of the dangers of black ice," he said.
In Eastern Europe, the death toll from a severe cold spell has risen to 71, most of them homeless people.
Temperatures dropped to minus 30 degrees in some regions, causing power cuts and traffic chaos and prompting authorities to close schools and nurseries.
Ukraine alone reported 43 deaths. The Emergency Situations Ministry said that 28 people were found dead on the streets, eight died in hospitals and seven in their homes. Over 720 others were hospitalised with hypothermia and frostbite.
More than 1,730 heating shelters have been provided across the country where the homeless people can get warm and eat hot food, including boiled potatoes, pork fat (a traditional Ukrainian dish), tea and coffee.
Hospitals were told not to discharge homeless patients even if their treatment was finished to save them from the cold
Some experts suggested the high death toll from the cold was linked to authorities' unwillingness and incompetence in dealing with the homeless.
Pavlo Rozenko, an expert on social policy with the Kiev-based Razumkov Centre, said Ukraine suffered from the Soviet legacy of viewing the homeless as alcoholics, drug addicts and do-nothings who need to be punished and locked away from society instead of helped.
"The country doesn't know yet how to take care of its homeless," he said.
Cold deaths were also reported in Poland, Romania, Serbia and Bulgaria.
In Russia, only one death in Moscow was attributed to the cold, even though temperatures fell to minus 21C.