The cold weather is set to continue over the weekend with northern areas most at risk of more snow.
The Meteorological Office in the North warned of more sleet and snow to come over the next couple of days. As well as causing further traffic problems, this is likely to lead to several sports fixtures being postponed.
Forecaster Michael Cleary of Met Éireann said that in terms of snow, counties in the Republic had "probably seen the worst of it for now. That's not to say that there will be no snow showers but they'll mainly be in northern areas or on higher ground".
Met Éireann recorded the deepest fall of snow yesterday of 2cms at its weather station in Birr, Co Offaly. But it said there was deeper snow on high ground where strong winds were resulting in drifts of up to 10cms.
Connacht, Ulster and parts of the midlands were worst affected by blizzards. However, sub-zero temperatures early yesterday caused freezing fog and black ice on roads in many other places as well.
In Co Wicklow, the Sally Gap was impassible due to snow and gardaí were advising motorists to avoid the Wicklow Gap. Driving conditions remained hazardous into the afternoon in parts of counties Cavan, Wicklow, Meath, Kildare and Donegal. Some snow also fell in Co Wexford.
The National Safety Council (NSC) has advised drivers to exercise extreme caution on the roads and to postpone non-essential journeys.
"Check local weather reports before you set off anywhere and if weather conditions are really extreme try to postpone your journey. But if you have to set out drive with care and caution," Brian Farrell of the NSC said.
The cold weather may have caught people unawares, coming so early in the season, Mr Farrell said and this could be an additional factor in accidents. "Coming on the back of a mild spell there's a danger this early cold spell will catch people out. We're urging people to tailor their driving to match weather conditions."
Temperatures are likely to be slightly higher today than yesterday - creeping up to five or six degrees in places, but it is to remain close to freezing at night.
The high winds which prompted Met Éireann to issue a gale warning yesterday will have died down considerably by tomorrow, according to Mr Cleary, and although daytime temperatures will remain quite low, it is likely to feel warmer. Sunday night, however, will be cold.
"You get frost at night as a consequence of the winds dying down, so it could be even colder at night than it has been," he said.
The cold spell is expected to end by Wednesday, but the warmer weather is likely to bring rain.
The cold spell in the North came as 15,000 primary school children were yesterday sitting their 11-plus exams. Teachers, parents and invigilators ensured that most of the children were able to take their exams, although it is understood that a small number were unable to sit the tests.