Does one freeze more easily when one is tired and why? I would like an
answer with credible scientific references. Many thanks :-)

When you are tired, your blood circulation and metabolism are lower -
your system resting and recovering -  and since the flow of blood
on/under your skin is reduced it is not passing inner body heat to the
surface as much as at other times, and you are more aware of the cold.
When you are active, the reverse is the case, sports for example, and
you are quite comfortable running around in just a t-shirt.

Also, when tired there is less sympathetic activity, and so less
activation of alpha receptors (which constrict peripheral blood
vessels when activated), and thus more heat is lost peripherally
(myoarin got it backwards). During excercise peripheral vessels
constict, which actually decreases blood flow and preserves heat, but
metabolites of excercising muscle will take precedent over sympathic
innervation (via adenosine receptors, etc.), so vessels dilate, thus
causing greatest blood flow to only actively working muscle.

Furthermore, in deeper stages of sleep (not REM) your body temperature
is unregulated and body temp drops (this actually helps sleep, which
is why some people sleep better by leaving a window open or
something). Hope that helps.