You are right. When certain nerves are compressed you can have blood flow cut off or decreased to a certain area even if your blood vessels are not constricted. Everything in our body is controlled by our nervous system. Incorrect signals can cause constriction of vessels causing cold hand...etc.
love and hugs,
Victoria
also..you need to rule out the vascular first then you will know if it is neurogenic...so doppler etc testing to see if it is a vascular problem!!