Whenevery my husband gets extremely nervous/stressed his veins start to turn greyish and he often complains of a burning sensation. Is this dangerous?

Sympathetic surge. This sounds like a stress reaction that causes over activity of the sympathetic nervous system. This can cause surge in blood pressure, increased flow of blood into head and neck with distention of the bluish draining veins in the face and neck. This can cause stress on the heart and predispose to heart attack or stroke. He needs a thorough medical evaluation. He needs stress reduction.