The Met Office has issued a weather warning for the county, with the strong winds expected between 1am and 11am.
A Met Office spokesman said: "A spell of very windy weather is expected during Wednesday, with the west to northwesterly wind likely to gust 60mph in places, locally 75mph over high ground.
"Some disruption to road travel is likely, including restrictions on bridges.
"The strongest winds will affect some of the higher level roads, for instance those over the Pennines and the Southern Uplands.
"However, the northwesterly winds will also be very strong and gusty at lower levels too, including in areas to the east of high ground."