A status yellow snow/ice warning has been issued for Donegal, Leitrim and Northern Ireland.
Met Éireann has said there will be wintry showers in the two counties during Sunday with some accumulations possible.
It also warned that there is a risk of icy stretches on untreated surfaces.
The warning is in place from 6am Sunday until 8pm Sunday evening.
In Northern Ireland, the Met Office has also issued a status yellow snow and ice warning for Antrim, Armagh, Down, Fermanagh, Tyrone and Derry.
Icy surfaces are likely in many parts bringing difficult travel conditions, it said.
The warning in the North is in place from 3am Sunday until 3pm on Sunday afternoon.
A second status yellow snow and ice warning will then come into force at 6pm on Sunday and will last until 10am on Monday.
“An area of rain, sleet and snow will move south through Sunday night with the potential for icy surfaces and some travel disruption,” the Met Office said.