The alert runs from 4am tomorrow, Thursday, January 28, until 3pm that day, with heavy snow expected to lead to some travel disruption and a chance of flooding.
It has also said some roads and railways are likely to be affected with longer journey times by road, bus and train services
The forecast says: “A band of rain will move north on Thursday and turn to snow over high ground.
“Snow is likely to low levels at times, but will mostly settle over higher ground above 200 m with 2cm to 5cm likely quite widely, while some places above 300m may see 10cme to 15 cm.
“There will be less cold air following the snow could lead to some thawing and localised surface water flooding on a few roads.”
The forecast for the county later on today states it will be a cloudy and damp night with a band of rain arriving from the southwest during the early hours, turning to snow on the hills, with the minimum temperature 2C.
Tomorrow, a band of rain and snow will continue to move slowly northeastwards during the day with some significant snowfall on the hills, but not exclusively.
Snow will turn lighter and patchy overnight and the maximum temperature will be 3C.
The outlook for Friday to Sunday is for rain and the snow will gradually ease on Friday with widespread severe frost overnight.
It will be dry, sunny and cold on Saturday and early Sunday, before rain and hill snow arrives later.