But not all cases. Exercise in cold water can generate enough heat to match or surpass the heat you lose, depending on water temperature in some work, and in other work regardless of temperature. Arm and leg exercise prevents a fall in core temperature benefiting individuals with a low shivering response. Exercise prevents core heat loss particularly in fatter subjects again demonstrating the benefit of body fat in keeping warm. It is noteworthy that these studies are all of subjects exercising in cold water with no protective garments.
Divers wearing exposure suits are more likely to benefit from the heat generation of exercise.
It is also possible to overheat, as swimmers doing laps in warm pools and divers sweating into their masks can tell you. A recent Navy study looked at overinsulated divers swimming in cold water and found they needed a bit of heat extraction to prevent overheating. If it were like sea water, you could safely drink sea water, which is not the case. Sea-going birds such as penguins, sea gulls, and albatross can drink sea water. Special glands in their heads excrete excess salt.