Oops, it doesn't look like 'no hat day' is a national day..

Other days

artists

Artists Day
comfy

Comfy Day
kiss a brunette

Kiss A Brunette Day
cat girl

Cat Girl Day
kiss a ginger

Kiss A Ginger Day
china

China Day
ruby

Ruby Day
stress awareness

Stress Awareness Day
unicorn

Unicorn Day
camera

Camera Day