The Met Office is expecting the drizzle to clear into Saturday and the sun should shine down on Yorkshire for a time.
Things won't be as nice on higher ground, where hill fog and stronger winds will persist.
The full Met Office forecast for Yorkshire:
Mostly cloudy and breezy with outbreaks of rain developing from the northwest during the course of the day. Temperatures rising but still feeling quite cold. Maximum temperature 7C.
Remaining cloudy overnight with hill fog and further outbreaks of rain at first. Turning drier through the night but still with some light rain or drizzle in places. Minimum temperature 4C.
Rather cloudy with hill fog persisting over parts of the Pennines and North York Moors. Mainly dry with some brighter spells likely at times through the day. Maximum temperature 8C.
Outlook for Sunday to Tuesday
Sunday, mainly dry with bright spells. Monday, windy with rain for a time. Clearer, colder conditions following. Tuesday, bright, cold and windy to start, clouding over with rain possible later.