Scotland is due to bear the brunt of Storm Caroline but shortly after 2:00pm on Tuesday, Met Éireann issued the weather warning of wind for counties Donegal, Galway, Leitrim, Mayo, Sligo, Clare and Kerry.
Met Éireann said Thursday will be bitterly cold overall, with gusty north to northwest breezes bringing showers over parts of Ulster, Connacht and west Munster by the afternoon.
"With cold air in place, a spell of snow looks likely to develop on its northern edge".
Sunday's weather warning is in force from 04.00 on Sunday until 23:55.
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Forecasting snow showers in the United Kingdom can be quite challenging as conditions are often borderline between rain and snow.
Tomorrow the Yellow weather warning for snow and ice is valid from 00.05 on Friday to 18.00 on Saturday.
Severe gales and snow showers have caused travel disruption, school closures and power cuts as Storm Caroline sweeps in to the UK.
In a yellow warning, the forecaster said: "Gusts of 60-70 miles per hour are expected quite widely, with gusts to 80 miles per hour possible near north facing mainland coasts and across the Isles".
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Road, rail, air and ferry services may be affected as cancellations are likely.
An North Sea oil rig, off the north-east coast of Scotland, is being partially evacuated over fears extreme waves caused by Caroline could endanger workers.
It covers much of Scotland, Northern Ireland, Wales and parts of northern and western England.
Gritters and patrols will also be deployed across the trunk road network with up to 8in (20cm) of snow and blizzard conditions forecast for higher routes on Friday and Saturday.
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"During winter weather which brings snow showers, it is not uncommon for snow amounts to vary considerably across short distances", said the Chief Forecaster.