Hats seem to be one of the more personal pieces of gear. People seem to care about the style of their hat than many other clothing items. There are a huge number of options with a wide variety of styles, colors, materials, etc.
Hats are highly effective at fine tuning thermal comfort because they are easy to put on and take off (provided you aren’t wearing a helmet) which lets you control the venting of a significant amount of heat. Hats have a good warmth / weight ratio so don’t try to save weight by skimping on your headwear. I would also strongly recommend that at least one of your jackets have a hood.
In hot weather a hat can help you stay cool and protects against sunburn.
When running I wear a basic Nike Dri-Fit Visor to keep sun and sweat out of my eyes. I generally use a Tilley LTM6 Hat which I think is one of the most versatile and durable hats on the market. I also have a Ultrafino Santa Fe Hat which I used what I need something more “stylish”. I sometimes use a Montbell Umbrelo when I am trying to stay cool in the rain. I generally use the hoods of my garments for warmth. I sometimes use a PolarBuff: in moderate conditions I double the fleece section over my ears with just the light polyester fabric over the top of my head to avoid overheating. When the temperature is down around freezing I reconfigure the buff so the fleece covers all of my head. When it gets really cold the buff becomes a neck gaiter / face mask inside my hood.
Many people use baseball caps to keep their hair out of the way, things out of their hair, and shading for their eyes. I don’t wear baseball caps because they don’t provide adequate sun protection for the side of my face and neck.
There are several companies that add a veil to a baseball cap to protect ears and neck from the sun. These hats provide very effective sun protections. The downside is that when using the veil, the wind is blocked which allows heat to build up more than if there was completely free air flow. I think the OR SunRunner Cap is one of the best options with a removal veil that is very packable. Sometimes rather than a baseball cap shape, hats have a higher crown like the hats made famous by the french foreign legion.
I have found the “coolest” wearing hats are classic loose weave Panama straw hat, which actual come from Ecuador. These hats provide sun protection while permitting better air flow than nylon or cotton weave hats. The down side is that they are more expensive, less durable, and can be a challenge to pack. There are some which will roll, but if you do that too often the hat will start to wear out. These hats degrade quickly if repeatedly worn in the rain. Note: most straw hats are highly woven which don’t permit a lot of airflow.
I have found the hats from Sunday Afternoons, especially the Adventure and Sports models with a veil in the back permits a reasonable amount of air flow while providing the best sun protections I have found. One downside is that the larger models have too much surface area without enough structure to work well in wind. The other problem is that I think they are one of the more silly looking hats on the market.
There are a host of more conventional brimmed hats on the market. I tend toward hats which have reasonable stiff brims such as the famous Tilley LTM6 Hat, the Shelta Hats Firebird v2 and Sunday Afternoon Charter hats. Dorman-Pacific makes a number of nice hats from a very light weight supplex weave which breaths somewhat while providing good sun protection. I like hats that have oval shaped foam brim with a plastic or wire stiffener running around the outside of the brim to keep it from flapping in the wind. Wallaroo makes some nice straw hats.
The Kavu Chillba is a modern interpretation of the asian conical hat which can provide excellent protection from rain and sun while permitting good ventilation. The Montbell Umbrelo is a packable rain hat in a similar style.
Another option is rather than using a hat, using a light weight hoody, combines with a visor to shade eyes, and maybe that face. The challenge is to find a hoody whose material provides good sun protection, air permeability, and is adequately durable. I have yet to find a hoody that I have been fully satisfied by.
In hot weather a cotton bandana, or better yet, a “tie” filled with poly-crystals such as those made Kooltie can help keep you cool.
In moderate weather having a hat which is wind resistant can be a big aid to regulate your body temperature. In cool or cold weather, hats made from waterproof breathable material can be quite useful. Outdoor Research is well known for making brimmed hats from WP/B materials. These sorts of hats can keep your head dry when you are not wearing a hood which allows more ventilation then wearing a hood which is nice in warmer conditions. There are a number of companies that make baseball style hats out of WP/B materials. Some people use these sorts of hats without a hood, or sometimes as a way to compensate for a hood which lacks an effective brim. Keep in mind that not all WP/B materials are equally breathable. If possible, get a hat made from eVENT. The classic OR Seattle Sombrero is one of the most beloved rain hats. I used one for many years.
In cold weather you will want a hat which keeps you warm. Winter hats can be caps (typically wool, fleece, or soft shell) though there is the blackrockgear downfill beanie, hunter style (typically shelled fleece), or balaclavas (normal fleece, windstopping fleece, high loft). I typically find a balaclava overkill until it is below 20F and windy at which point it is indispensable. The Mountain Hardware Flex balaclava is my favorite. Don’t underestimate how much a neck gaiter (or scarf) can help you stay warm.
Details and Further Information
There is a wide range of numbers given for how much heat is lost through the head. My investigate of various scholarly articles brought be to the conclusion that somewhere around 10% of body heat exits through the head & neck given uniform insulation on the body. This changes significantly when you are shivering / approaching hypothermia where you lose around 45% of your heat through your head.
Get a free hat. Lots of companies give hats away with their logo on them for proportional purposes.