Met Éireann has extended a status yellow ice warning to all counties, effective from 7pm on Wednesday until 12 noon tomorrow.
Forecasters warn of icy stretches leading to hazardous travelling conditions.
They say wintry showers will continue, with freezing rain possible in the southwest. They also predict freezing fog patches.
While travel in urban areas may not be affected, travel to schools in rural areas could be hit. Decisions are taken locally on whether buses can operate, and whether schools can open.
According to Bus Éireann, which operates the school bus scheme, overall, a small proportion of school transport routes didn’t run today, but the disruption was more widespread than was the case yesterday.
There will be sporadic falls of snow, sleet and rain throughout Wednesday, with snow most likely in the north and west. Isolated hail and thunder is also possible into Wednesday evening.
Temperatures are expected to drop to -4 nationally but Met Éireann have warned it is likely to be colder locally in parts of Ulster and the North Midlands.
A widespread frost will develop with icy stretches leading to hazardous driving conditions, the forecaster said.
Outbreaks of hail and sleet will cover parts of Munster and Connacht overnight and into Thursday morning while patches of freezing fog will also develop.
“As the day goes on it will become mostly dry and bright, although some patches of mist and fog may linger as winds stay light and variable. Cold with highest temperatures of 1 to 5 degrees.
Thursday night is similarly expected to be a bitterly cold night with lows of -4, and colder locally, with rain, sleet and fog all forecast for Connacht, Munster and southern Leinster.
Met Éireann have said the outlook is for chilly weather to remain until the weekend but temperatures will rise a few degrees on Saturday.
Rain and sleet will persist on Friday but the night will not be as cold as recent nights with lows of -1.
Saturday will see temperatures climb to between seven and 11 degrees, with Saturday night not being much colder than the daytime. It will be a dull day with rain and drizzle predominant in most parts of the country.