Menthol is the "cooling" chemical in mint. It doesn't actually cool anything. Rather, it sets off the TRPM8 receptors that your body uses to detect cold, much as capsaicin (in chili pepper) does to the TRPV1 receptors for detecting heat.
Drinking water is usually colder than body temperature. So you get the "real" cold sensation from the water, plus the "fake" cold sensation from menthol hacking your nerves.