I rarely wear a hat. I will wear a bucket hat on a hot sunny day. I might wear a winter hat if I'm not wearing a hooded coat in winter. I have one with a peak and ear flaps, that can fit in a pocket. It is supposed to be waterproof I think, made by Sealskinz. Apart from those extremes, just a cycling helmet, with a cycling cap underneath (not peaked, just a season appropriatee skull cap) when on my bike.