Latest: Gardai say driving conditions are poor on three major motorways in the midlands.
Emergency services are clearing a collision on the M8 between Junction 3 and 4 Northbound, they said.
They've warned motorists to take particular care on the M4, M7, and M8, with motorists asked to exercise caution and reduce speed.
Meanwhile, the N81 is impassable at Citywest in Dublin this evening due to very poor road conditions.
Gardaí are advising road users to use an alternate route.
The Dublin Regional Homeless Executive has activated its emergency plan following the snowfall this afternoon.
Extra outreach teams are out, and additional accommodation is being made available.
Updated at 8:23pm with details of Citywest road conditions.
Earlier (5:35pm): Snow and sleet has caused travel disruption across the country amid a number of weather warnings.
A yellow warning for snow and ice has been issued by Met Eireann for all of Leinster and Co Tipperary. It is in place until 8am on Monday.
Heavy rain, over much of Leinster, Munster and parts of south Ulster, will continue to fall as sleet and snow in places, giving some accumulations of snow and poor driving conditions. But mainly dry in west Ulster and west Connacht. Gusty northerly winds along the south coast. pic.twitter.com/9lMoCGJLyw— Met Éireann (@MetEireann) March 3, 2019
There was a similar status of warning for heavy rain in Leinster and Munster during Sunday morning and afternoon as Storm Freya hit southern counties.
The AA urged caution on the roads, particularly on higher ground.
The organisation reported bad driving conditions in counties Kildare, Tipperary and Laois.
“Driving conditions are extremely poor on the M7 and M8 with snow and ice on the road,” it said.
“Snowfall is also affecting visibility. Gardai advise road users to avoid using these stretches of road if possible.”
There were also reports of hazardous conditions in Cork, Kerry and Wicklow.- Press Association
Met Eireann have issued a Status Yellow snow and ice warning for 22 counties.
The forecasters expect today's heavy rain to turn to sleet and snow from around noon today.
They say that Munster, Leinster, Cavan, Monaghan, Galway and Roscommon will see a dusting of snow at lower levels, but much of the snow will be above 200 metres.
Snow-ice warning issued
Areas: Munster, Leinster, Cavan, Monaghan, Galway and RoscommonMarch 3, 2019
However, wet and slushy roads are likely to become icy in places overnight as temperatures drop below freezing.
The warning is valid until 8am tomorrow morning.
It comes as Munster and Leinster experience a Status Yellow Rainfall warning until 6pm this evening. Up to 35mm of rain has been forecast for the area.