On average, both December and January have 23 of their 31 days considered cloudy -- as in at least 80 percent of the sky covered on average through the day. November is right behind with 22 of 30 days as cloudy.
But, November can lay claim to fame as the least sunniest month, with only 2 sunny days on average -- compared to 3 days for January and December. (It makes up the balance with one extra partly cloudy day over January and December.)
Both December and January also hold the title for cloudiest month ever. Imagine this: the sun goes the entire month without an appearance. That occurred both in Jan. 1953 and Dec. of 1966.