Rain will begin to spread from the south today and this will start the melting process with potential flooding.
Some snow this morning, widespread treacherous surfaces due to ice and lying snow.
Matthews, who run 133 services a day between the north east and Dublin, say the company will continue to review the situation and passengers will be kept updated through the Matthews.ie Facebook page.
Meanwhile, there is a status yellow Snow-ice Warning for Connacht and Donegal.
The decision was taken by forecasters in Met Eireann at 11pm on Wednesday night over the threat of snow and ice.
Gardaí are advising drivers not to make any unnecessary journeys as many roads remain risky until they are cleared of snow.
A strong easterly gale has caused tidal flooding in low-lying areas of South Dublin and Wicklow.
It is unclear just how much snow has fallen in parts of the country but Met Éireann has estimated that up to one metre could fall in parts of Dublin.
There are now risks of localised flooding as the snow melts.
Some 22,000 homes, farms and businesses are still without power this morning.
The Government has lifted the advice for people to stay indoors - however they should still use their own judgment as to when is safe to go out.
Education Minister Richard Bruton said schools and colleges across the country will reopen on Monday "where possible". Temperatures may drop to as low as -3º.
"Monday, we'll see some dry, bright spells, but cloudy, misty periods also, with some scattered showers".
"Snow continuing to thaw with some rain for a time overnight, but dry, cold and clear later".