Met Eireann is predicting snow and wintry falls this week but Tuesday is set to be a damp and misty day with outbreaks of rain and drizzle.
Sunny spells and scattered showers will follow as the rain clears for the rest of the day becoming mainly dry by evening.
Temperatures of 13C will drop to a low 2C overnight but will remain mostly dry, turning chilly early on in the night.
It will be cold and blustery on Wednesday with sunny spells but showers will spread from the west during the day.
The showers will merge to longer spells of rain later in the day and some wintry falls are possible on high ground.
Highest temperatures of 9C will drop to a low -1C with clear spells and scattered wintry showers overnight with snow in parts with some frost and ice possible also.
For Thursday, they added: "Cold and windy on Thursday with sunny spells and widespread showers and longer spells of rain at times.
"Further wintry falls in parts, mainly on high ground. Strong and gusty west or southwest winds with gales at the coast.
"Maximum temperatures of 6 to 9 degrees. Clear spells and scattered showers overnight with the strong westerly breeze beginning to ease. Minimum temperatures of 1 to 4 degrees with some frost."
A Weather Advisory is still in place for Connacht, Longford, Offaly, Westmeath, Cavan, Donegal, Clare, Cork, Kerry, Limerick and Tipperary.
This means: "Periods of heavy rainfall from Saturday to Tuesday may lead to some local flooding as river levels remain elevated.
"The heaviest of the rain will be through Saturday afternoon, and again early Monday and early Tuesday, with rainfall accumulations from Saturday to Tuesday of 40 to 50mm in places, with some spot flooding."
This warning is valid until 6pm this evening.
