Met Éireann has issued a status yellow weather warning with air temperatures expected to drop to between zero and minus 4 degrees tonight.
The warning will be active from 8pm tonight until 10am tomorrow morning, with widespread severe frost returning.
People making journeys have been warned of slippery paths and dangerous roads.
Gardaí say there was noticeably less traffic on many roads, as motorists heeded warnings to avoid non-essential travel.
Vehicles from Transport Infrastructure Ireland gritted motorways and national roads overnight as temperatures dropped as low as minus eight degrees in parts of the west, midlands, Leinster and Ulster.
Many local roads around the country remain icy, with some not expected to improve until tomorrow.
The cold snap resulted in the closure or late opening of dozens of schools in the midlands and the west. Many are expected to open as normal tomorrow.
Homeless charities said they were making extra efforts to ensure that anyone who needed a bed overnight would receive one.
Community groups in rural areas have appealed to residents to look out for older neighbours, in particular those who live alone.
There was disruption to flights between Britain and Ireland, with dozens of flights cancelled because of snow, with dozens more delayed.
Passengers are being advised to check the flight status before they travel to the airport.