When cold or in shock a person's blood vessels constrict in order to preserve heat or to move blood flow to protect vital organs. I am interested in the mechanism by which this is achieved. Does this occur along the entire length of the limb or are there 'pinch points' (for example is it possible to simply have a point of vasoconstriction just below the shoulder which would reduce blood flow to the entire arm)? Am I correct in thinking that the response is neurological rather than endocrinological ?
Reduced blood flow to a region of the body occurs through 2 principal mechanisms.
1) The smooth muscle fibers in the tunica media layer of the arteries contract and reduce the diameter of the artery, limiting blood flow due to increased resistance (this is the mechanism in @agrimaldi's answer).
2) Circularly oriented smooth muscle fibers at the junction of a metarteriole (the distal end of an arteriole) and a capillary bed form a precapillary sphincter, which serves as a valve and prevents blood flow into a the capillary bed.
So to answer your question, it is both. The narrowing of the arteries would occur rather continuously across the limb but there are "pinch points" where metarterioles joint the capillary beds.
The endocrine and nervous systems are pretty integrated so in most cases it would be the result of the actions of both systems.
Vasoconstriction is a phenomenon that can be caused by many factors, from mechanical events (such as stretching) to hormones (epinephrin, neurepinephrin, angiotensin ...). But no matter what is the cause, the end-result is an increase in intracellular calcium concentration in smooth muscle cells (which compose the arteries and veins). So it seems that constriction does not happen in specific points but rather all along the limb. Furthermore angiotensin receptors are found in high concentration in smooth muscle cells , suggesting that every such cell has the ability to change it's morphology in order to induce vasoconstriction.
As for your second point, I think the response is as much endocrinological as neurological, since it involves both peripheral and central regulations. (Well, as a side note, endocrine systems rarely have no interaction with central ones).