By its name vasoconstriction causes blood vessels to contract and reduces blood flow. Blood carries heat from the interior of the body so if less blood is flowing to skin/periphery it gets cold and clammy.
I'd also like to clarify that vasoconstriction is a an effect of something (usually hypotension i.e. blood loss). The hypotension itself activates the patient's sympathetic nervous system which in the skin causes sweat production, hence the "clammy" skin part which is different from the vasoconstriction, which it also causes, producing the "cold" part.
yes it really makes sense, I had not remember that the sympathetic nervous system besides contribute to vasoconstriction,
also contributes to the clammy skin 🙂 Thank you again for the enlightening answer.