The Met Office warning is in force from 10am on Saturday until 6am on Sunday.
It states: "Heavy freezing rain is expected to develop during Saturday. This will result in the rapid formation of widespread ice on roads, pavements, trees and other structures.
"Freezing rain is rare in the United Kingdom but when it does occur the impacts can be very severe. This is due to the fact that it can form very quickly, it can be difficult to see and is incredibly slippery.
"Some sleet and snow is possible over the very highest ground and the freezing rain may also be followed by a spell of sleet and snow as the precipitation clears from the west.
"The freezing rain and sleet and snow will be accompanied by strong southeasterly winds which will pose an additional hazard to travel, in particular over high ground."
A yellow warning for snow and ice is also in place for the county between 9am on Saturday and 9am on Sunday.