A status yellow wind warning has been issued for Donegal, Leitrim, Mayo and Sligo from 5pm on Monday night.
Winds of 50km/h to 60km/h with of gusts of up to 100km/h are expected throughout the northwest.
The strongest gales will be on the coast.
The warning is in place until 6am on Tuesday morning.
Showers will become widespread early on Monday night, turning wintry over high ground. It will become blustery in all area with fresh to strong winds.
Ulster is set to be very windy especially in coastal areas. Temperatures are expected to drop to between 1 and 5 degrees.
Tuesday
Tuesday will be largely dry and sunny day. Highest temperatures of 7 to 9 degrees. The strong winds will gradually ease through the afternoon.
Wednesday
Another dry day on Wednesday but it will be quite cloudy with maximum temperatures of 7 to 10 degrees. The cloud cover will keep the temperatures from dropping below freezing in many places, but there is a risk of frost in some areas.
Thursday
Thursday will be a largely dry and cloudy with temperatures from 9 to 11 degrees with moderate winds.