Visor?

Yep, I've abandoned my hat collection in favor of "Headsweats" visors (at least in the summertime). Much lighter and I combine the visor with cotton handkerchiefs soaked in water in intense heat and sun. I live in Arizona and hike in 90- 100 degree weather. Headsweats are washable and last a long time if you care for them, come in colors and keep the sweat out of my eyes with their terrycloth lining. The headband comes in two styles, one is elastic and takes a while to loosen up but is fine, the other is adjustable like ball caps.

I've been using a Headsweats visor for local hikes this summer. The non-adjustable one does take a while to loosen up, but it's good otherwise. The whicking material is very comfortable and keeps sweat out of my eyes. I have a white one with black on the underside which helps with glare. Better than any visor I've used in the past. I still take a Sunday Afternoons hat for overnight trips.

I've been using a visor for years and much prefer it to a hat. It's just way more comfortable and breathable than a hat, and yeah, less material to soak up moisture. I like mine paired with a thin baselayer hoody for extra sun protection, but there's so few good hoodies like this that I'm looking for a better all around sun solution. I'm on my second montbell visor, which is great, but sadly I don't think it's available any more.

I sometimes use a ballcap sometimes use a visor.
Visor is lighter, more breathable, but it’s not that good in windy or rainy days. So I usually bring a big enough square scarf with my visor. When it’s sunny, I use the scarf to protect my neck and side face from sun; when it’s windy or rainy the scarf provide some protection for my head.
BTW, I also use the scarf as a towel, and use it to wipe off the condensation on the tent.

I live in Florida. A visor is much cooler than a ball cap. If I need sun protection I use a buff which in my opinion is very breathable. Ive tried wearing a ball cap but heat up too quickly while hiking.

When I'm not wearing a Tilley, I wear a visor. I like the Adidas Adizero II.

My dermatologist would not recommend the headsweats and other ball cap designed headwear. She says they don't give enough protection to the face, particularly near the cheekbone area. She sees a lot of skin cancer on the upper sides of the face.

She would recommend a visor with a broader, wrap around design that keeps the upper sides of the face shaded.

Jang-Tian, what is your scarf made of?

I'm not sure I should call it scarf or head cover or handkerchief. Anyway, the square fabrics I use are made of cotton which not only absorbs water quickly, but also dries quickly since it’s thin enough. I've owned some with different thickness, the thicker they are the more water they can absorb making them better as a towel. The thinner they are, the faster they dry. The yellow one in the pictures below is my favorite which has a good balance between quick dry and water absorption ability. BTW, it would be better if it's a bit larger.