>>As for hypothermia, I don't know how important the head is versus the body.<<

Vastly. Huge importance. Critical.

And much more so than any other "appendage". The body reacts to cold by quickly cutting down the blood flow to limbs (especially the surface where heat dissipates) and even organs, and can make LARGE adjustments to heat loss by doing so, will even sacrifice appendages (toes lost to frostbite) if it has to, but it CANNOT restrict blood to the brain for obvious reasons. This is such a critical factor that we not only still have a mat of fur on our heads to help regulate heat loss, but it can be grown to any length... and odd development, when you think about it.

In some spectral ranges of infra-red, people wearing down jackets in the cold look like matches with their heads alight- the amount of heat leaving from the head is amazing. Same applies to a head sticking out of a sleeping bag.

I always carry a lightweight balaclava when camping; it makes more difference to sleeping well in the cold than a LOT more weight in a sleeping bag.

When ambient temperature raises significantly above blood temperature, things reverse, and the insulation (hat, cap, hair) actually helps keep the head cooler than surroundings. Having the surface that the sun beats on as far away from the brain as possible helps too, hence sombreros and ten-gallon hats with high crowns.

JFK refused to wear the traditional Homburg hat to his inauguration, starting a fashion stampede away from hats. Actors suddenly found that their faces were much more visible on movie screens without hats, and, since Hollywood dictates style, and then the car makers immediately took advantage of the trend to lower their roofs (and costs) there was no going back from there... but it's a huge disservice to those who go outdoors. Real outdoorsmen wear hats, or at least have one (or more) in their kits. Properly used (take it OFF when you start to get hot, out of the sun), a hat can make amazing adjustments to your comfort level and safety- there's a reason men have worn them for at lest several thousand years. The lack of one can certainly kill you in the desert, and might make the difference between life and death in the cold.

Thanks for the tip about the mylar in a hat- I hadn't thought of that, and at the risk of comments about geeks and tinfoil beenies, I might play with the idea a bit. Tilly hats have this convenient little pocket in the crown...