Apperently...
You can lose 40 to 45 percent of body
heat from an unprotected head and even
more from the unprotected neck, wrist,
and ankles. These areas of the body
are good radiators of heat and have
very little insulating fat. The brain
is very susceptible to cold and can
stand the least amount of cooling.
Because there is much blood
circulation in the head, most of which
is on the surface, you can lose heat
quickly if you do not cover your head.
- FM 21-76 US ARMY SURVIVAL MANUAL, BASIC PRINCIPLES OF COLD
WEATHER SURVIVAL, PG 148.
Can this be right ? Does more body heat escape from our heads than from other parts of the body ?
Short Answer: No.
In general, heat loss is essential to
provide thermoregulation and prevent
excessive heat build-up in the body to
avoid the consequences of heat stroke.
However, heat loss in the head is the
same as for any exposed body part. The
exposed surface area of the body,
along with relative humidity and
temperature, determines heat loss
primarily through evaporation and our
head makes up only 10 percent of body
surface area. So, at rest, heat
loss through the head accounts for
only 7-10 percent of total heat
dissipation. - source
See below: General heat loss through the head.
EXCEPT...
As you begin
exercise, cerebral blood flow
increases due to increased cardiac
output and the percentage of heat lost
through the head accounts for about 50
percent of total body heat loss. As
exercise continues, more oxygen is
directed toward muscle and blood flow
to this tissue increases. Core
temperature has to be maintained and
as body heat increases, the skin
arterioles expand, or vasodilate,
redirecting blood flow to the skin
which cools the blood. Hence, total
blood flow to the brain is decreased
and the percentage of total body heat
lost through the head is reduced to
about 10 percent. The percent lost
through the scalp returns to 7 percent
after sweating begins. - source
Shivering is exercise...
But, this is important, if they are
shivering, the percent of heat loss
via the scalp can increase to upwards
of 55%, so protecting the head well is
a very important part of treating the
hypothermia patient. And as you can
imagine, the primary defense against
the cold and hypothermia is
vasoconstriction of the peripheral
circulation, this shunts blood to the
core, reduces circulation to the skin,
and increases the percent of heat loss
through the scalp. - source
General heat loss through the head
source: Thermal effects of whole head submersion in cold water on
nonshivering humans
One hypothesis predicts a substantial
heat loss through the head due to the
great amount of surface blood flow in
the scalp and because scalp blood
vessels do not vasoconstrict in
response to cold as do surface vessels
in other body areas (8). An
alternative hypothesis predicts
minimal heat loss from the head
because submersion of the head and
neck would only involve 7–9% more of
the body surface area (20). As well,
mathematical modeling predicts minimal
conductive heat loss directly through
the scalp and skull (27).
The present results are consistent
with previous data (9) in that the
supposition of proportionately greater
heat loss from the head was not
supported.

Whole body cutaneous heat loss
(n = 8) values for baseline (20 min)
and immersion (30 min) periods.
*Greater than body-insulated conditions, P <
0.001. †Greater than head-out in the same subconditions, P < 0.05.
The measured heat loss from the head
in both head-in conditions was only
100 kJ (compared with 17 kJ in the two
head-out conditions). In contrast,
total heat loss in the body-exposed
configurations was 914 and 988 kJ, for
head-out and head-in conditions,
respectively. In the latter case, the
head accounted for only 10% of the
total body heat loss when both the
head and body were submersed. The
surface area of the submersed head is
7% of the total surface area of the
body.
Energy
production and loss during 30 min. of
immersion in 17°C water (n = 8). Total
loss includes whole body cutaneous and
respiratory heat loss. Body loss
includes trunk, legs, and arms.
*Greater than body-insulated conditions, P < 0.001. †Greater than
head out in the same subconditions, P
<
0.005. ‡Greater than head-out conditions, P < 0.001.
These results thus indicate that heat loss from the head is not
disproportionately increased over what
would be expected from the head’s
contribution to total body surface
area.
However...
With the body exposed to cold water
and shivering intact, additional
dorsal head immersion increased core
cooling from 3.8 to 9.4°C/h (250%) in
1–2°C water.
The Bottom Line...
Oliver_C is correct: "No, mom, Science says I don't need to wear a hat !..."
"...Ok, mom, I'll bring one along just in case I get cold !"
Cited and worth a read...
(8) Froese G and Burton AC. Heat loses from the human head. J Appl
Physiol 10: 235–241, 1957.
(9) Giesbrecht G, Lockhart T, Bristow G, and Steinman A. Thermal
effects of dorsal head immersion in cold water on nonshivering humans.
J Appl Physiol 99: 1958–1964 2005.
(20) Layton R, Mints WJ, Annis J, Rack M, and Webb P. Calorimetry with
heat flux transducers: comparison with a suit calorimeter. J Appl Physiol
54: 1361–1367, 1983.
(27) Xu X, Tikuisis P, and Giesbrecht G. A mathematical model for human
brain cooling during cold-water near-drowning. J Appl Physiol 86: 265–
272, 1999.