There have been many different studies on the use of a hat during athletics. There are two trains of thought, some feel wearing a hat outdoors may reduce the level of thermal stress by limiting the amount of solar radiation to the head, but others feel that covering the head may also impede convective and evaporative heat loss during extreme heat.
In my opinion, it is very important for an archer to wear the proper hat while shooting. A light brimmed hat helps protect your from the sun so you do not burn and more importantly provides shade to your eyes so you can see the target while you are at full draw. In rainy conditions, a brimmed hat has the additional benefits of keeping your head dry and protecting your glasses from raindrops.
It is important to find a hat that not only feels right and looks good but also does not interfere with the bowstring. For compound archers, their bows have a narrower string angles at full draw that enables them to choose hats with a larger brims such as a baseball cap. For most recurve archers the bowstring angle is much wider, and therefore they will need to choose hats with a shorter brim. A lot of recurve archers choose to use a bucket hat similar to the hat Gilligan wore on the 60’s popular TV show.
Finding the perfect hat for you is not always easy and may require some trial and error. Remember, the hat should have some shade protection for your eyes, some sun protection for your head, it needs to fit right, and feel comfortable, somewhat breathable, and most important not interfere with your bowstring. Even if you choose not wear a hat regularly while shooting, you should always have one with you, just in case.