Exposure to cold produces a cold diuresis (production of urine by kidney) and a reduction in blood volume as a means of controlling the transfer of heat to the body’s surface, keeping you warmer in a cold environment.

Cold Diuresis

http://www.globalbioweather.com/weather_cold_diuresis.html

"The body protects vital organs from cooling by reducing the blood flow to the outer layers of the body. More warm blood is kept in and around the body’s core, increasing the volume and pressure at the same time. Unfortunately, the brain may perceive this as an unnecessary increase. It instructs the kidneys to extract some of the fluids from the blood and shed it as urine.

Once the reason for the cold is eliminated, the blood flows back to the periphery. A frequent toilet trip, however, reduced fluid levels considerably and the body may experience mild dehydration."

These answers do little to explain why, getting a chill, or simply placing your hand under cold water at a sink, can cause the same effect, long before bodily organs have time to react.