The City had rain early in the morning the other day, turning to sprinkles by 10AM, and that is to my mind the perfect weather for a hat. Felt hats should not get soaked, but they do a fine job of keeping the head dry otherwise. Combine them with a winter weight suit and a scarf to cover the chest and a coat becomes unnecessary in 50-60 degree weather (10-15 degrees Celsius).
My favorite hat in brown beaver felt tops a gray flannel suit, blue silk scarf, navy and white mini-checked shirt, white linen pocket square and black semi-brogues. There is a dark purple cashmere necktie hiding beneath the scarf.