The GFS-P is showing widespread heavy snow for Tuesday from south Dublin to Limerick and southwards. The track of this low pressure will be crucial and could change quite a bit. If this tracks further north, rain would be more likely across the south, if it tracks further south, many places staying dry, until sleet and snow showers later in the
The GFS-P also showing plenty of snow across the country on Wednesday and more on Thursday and Friday. Perhaps the GFS-P is totally going overboard on the snow potential for Ireland over the next 6 days. Thursday and Friday is also very far away in terms of what could happen, so not much point spending too much time on those days just yet.
The operational GFS has Ireland missing out on that low pressure system on Tuesday with rain passing to our south. and wintry showers across the country later in the day.
As for Thursday/Friday the GFS has a marginal mix of rain and sleet across the country with hill snow.
If the GFS-P proves correct (which I think is unlikely), then there is a chance for disruptive snow in parts of Ireland from Tuesday onwards.