The forecaster warns of travel disruption, power cuts and icy paths and roads in the area from Monday at 6pm until Tuesday at 11.55pm.
The Met Office has issued a yellow "be aware" warning that states snow showers will be heaviest and most frequent across the Western Isles and Highlands on Monday through to Tuesday.
Met Éireann say that the fog will be most dense inland, away from coastal areas, and will lead to poor driving conditions, so if you are going to be on the road, you might want to allow a little extra time to get from A to B.
As well as this, a Status Yellow rainfall warning has been issued for counties Galway, Mayo, Clare, Cork and Kerry.
The weather alert has been valid since Thursday 12 noon and will last until Friday at 2am.
The remainder of today will be mostly cloudy with the chance for some sunny spells this afternoon. Top afternoon temperatures of 3° to 7° are given for the day. This will become more extensive again after dark.
But, as southeasterly winds freshen later tonight, the fog will thin and frost will tend to clear - but, there could be patchy drizzle as cloud will thicken, Met Eireann predicts.
Still remaining rather cold with highs of 6C.
The bad weather will continue in to Friday, with strong winds and a spell of heavy rain expected. Afternoon temperatures will range from 5° to 9°, while it will be coldest in the north.
Britain is wrapping up for another chilly night with temperatures expected to drop to freezing widely with lows of -2C (28.4F) or -3C (26.6F) in rural regions.