National Hat Day is celebrated in the United States every January 15th and is a fun excuse to wear a hat. You could post a photo of yourself wearing a hat, perhaps relating a funny story to go along with it. You could also invite your social media followers to post their hat photos using the hashtag #NationalHatDay.
In Australia, Hat Day is on the 2nd Friday in October, in support of and to raise awareness for mental illness.
In the U.K., Wear a Hat Day, in support of brain tumour research seems to be late March (27th March for 2020)