In a word: No. Not too long ago I wrote about the myth that you lose 40 to 45 percent of your body heat through your head. Turns out some people make even more grandiose estimates, saying that you lose up to 75 percent of your body heat through your head.
They're all wrong. Some experts theorize that you might feel the cold a little more acutely in your head because the scalp has so many blood vessels close to the surface -- but as far as actual heat lost, your head acts pretty much the same as the rest of you.
To paraphrase a survival instructor I heard speak on this topic a couple of years ago: If all the myths about heat loss through the head were true, you'd be completely comfortable in the cold with nothing but a hat on. Feel free to conduct your own experiment on this matter... or you could just read about the experiments that debunked the myths in the Wilderness Medicine Newsletter.
There are a few interesting details about how your circulatory responds to exercise and the net result in terms of body heat lost, but it all boils down to the same thing: Your head really isn't all that special when it comes to heat loss on dry land. If we're talking about water, though, that's a different story.
That said, the Yale Medical Group does warn that because a child's head is greater in proportion to the rest of his/her body mass than an adult's, they stand to lose more heat from said head -- so wearing a warm hat is particularly important for kids.
Got a hiking-related question of your own? Drop me a line!