Surface water and spot floods are causing problems for motorists this morning.
AA Roadwatch said that Dublin and Cork are worst affected, but conditions are steadily improving.
In Dublin, there are reports of flooding on Pottery Road in Dun Laoghaire, and at the intersection between the M11 and the M50.
In Cork, parts of Blackpool are impassable, and extreme care is advised on the N71 Cork to Bandon Rd between Inishannon and Ballinhassig.
[comment]Blackpool last night:[/comment]
Care is needed also in Co Wexford and in Waterford City, Dungarvan and Dunmore East.
Snow conditions on high ground in Wicklow, windy weather in Mulllingar and fallen trees in Laois, Clare and Sligo.
Arwyn Foley from AA Roadwatch said that there is a big improvement in conditions in Dublin, but Cabinteely and Dun Laoghaire are still bad, as is the M11 near Bray.
"Further south as you head towards Bray in Co Wicklow, there is flooding just south of the Bray North exit," she said.
"This means though if you're travelling south from the M50, you'd be forced to exit an Junction 16 Cherrywood, ad if you're coming from the N11, the Bray road from the Cabinteely direction heading towards Bray, you'd be diverted at the Loghlinstown roundabout."
"If you're travelling north on the M11, you'd be diverting at Junction 6 for Bray."
In the North, more than 18,000 homes are without power.
The runway at George Best Belfast City airport has been closed due to snow.
Passengers are advised to check with their airline regarding travel arrangements.
Irish Ferries later advised that due to adverse weather conditions on the Irish Sea today, all of its Jonathan Swift fast craft sailings have been cancelled.
That includes the 8.45am Dublin departure and the 11.50am Holyhead sailing.
All passengers booked on these sailings will be accommodated - those affected should contact Irish Ferries.
All other Irish Ferries sailings are expected to sail to schedule.