Met Éireann has warned that the current cold spell is set to continue for the next few days, with temperatures dropping as low as -4C overnight.
The forecast is for heavy snow showers in many areas especially across the northern half of the country leading to some "accumulations".
Lighter snowfalls are expected to clear during daylight hours however, there is a danger of sharp and severe overnight frost in all areas.
The bad weather has already affected some ferry sailings and flights.
The Irish Ferries Johnathon Swift sailings on the Dublin to Holyhead route were cancelled due to the weather however, all other sailings are expected on time.
A number of flights arriving at Dublin airport from London Heathrow and London Gatwick experienced delays and there were some cancellations.
Nicola Hudson of AA Roadwatch said although drivers were surprised to find their vehicles covered in snow this morning it did not stick on the roads for long.
She said: "Overall driving conditions were good and the overnight frost cleared quickly. There was a warning that snow would accumulate in Northern parts of the country and on higher ground but the Sallygap, Barnsmore Gap and Glenshane pass were all reported to be fully passable this morning".
AA Roadwatch is urging caution especially on high ground or exposed roads.
"With very low temperatures and frost forecast, it is possible that road conditions will be very dangerous.
"Motorists should take particular care when driving overnight and in the early hours of the morning," Ms Hudson added.
