Cold water help in many thing first it does increase your metabolism and also bathe in cold water help to make blood vessels constrict and may even aid to reduce swelling.
But the water shouldn't be too cold as that can cause broken capillaries instead. In addition, if you're removing makeup, it is recommended that you use warm water to remove the oil and sebum.
You may also like to know that using cold water as a final rinse for our hair can help close the scales of the cuticle, and can help constrict the openings of the sebaceous glands to help moderate sebum production.