Met Eireann is warning of sub-zero conditions until early next week.
Temperatures could hit their lowest next Tuesday at --5C .
Temperatures were expected to fall to below zero in many parts while strong winds and torrential rain made roads treacherous.
Met Eireann has warned of a band of snow across northern Leinster, Ulster and Connacht, with up to 10cm due to fall on higher ground.
Snow and sleet are expected today and tomorrow, with ground frost and freezing fog also expected.
Meanwhile, Gardai said there were a number of minor collisions on the M50 yesterday evening and in other parts of the capital as motorists grappled with the tough driving conditions.
The Road Safety Authority (RSA) is predicting a significant level of black ice across the road network.
"There's a real mixed bag of weather out there and back roads could be particularly dangerous," the RSA's Brian Farrell told the Herald.
"On a weekend like this, it is crucial that people take it easy when driving. The potential for black ice is much greater, which can create really treacherous conditions," he added.
Sections of the N11 were flooded as a result of torrential rain, while a number of roads across the eastern coast were rendered impassable.
A severe weather warning remained in place this morning amid fears that the blizzard conditions could cause havoc.
The weather conditions have also hit air and train services.
Aer Lingus was forced to cancel 16 round trips to UK airports yesterday because of the weather there.
Spokesman Declan Kearney said passengers are facing a wait-and-see situation today.
"It looks like conditions will improve over the weekend. We are certainly hopeful that we will run a full schedule today but we are advising customers to check our website in good time before departure," he said. A number of Ryanair flights to UK airports were also delayed.
Meanwhile, flooding at Sandycove in South Dublin caused a series of cancellations on the Dun Laoghaire-Bray line last night.
However Irish Rail said it is hopeful today's train and Dart services will be unaffected.
"A number of services were cancelled last night between Bray and Dun Laoghaire as a result of flooding on the track at Sandycove.
"Irish Rail staff monitored the flood levels but it is not expected that there will be delays on Saturday.
"However this can change; it is all weather-dependent," said spokeswoman Jane Cregan.
Bus Eireann said it would be monitoring routes over the weekend, but that services had so far been largely unaffected.
Met Eireann forecaster Joan Blackburn said that the blizzard-like conditions are expected to weaken today, but will continue over the weekend.
"All our indicators would suggest that outbreaks of sleet and snow will become more scattered. Temperatures will be very close to freezing all the time."
There were reports of flooding in parts of South Dublin and Wicklow on the N11, with Shankill, Greystones and Wicklow town most affected.
The Department of Transport has issued its own warning to road users who are advised to keep an eye of its website www.dttas.ie.
Dublin Fire Brigade reported a busy evening last night as its officers were braced for emergency call-outs.
Britain took the brunt of the weather with some 2,000 schools forced to close.
Some 25cm of snow fell in parts of South Wales, with 10,000 homes losing power.