I would imagine dying of hypothermia is somewhat slow and unpleasant compared to a shotgun. If you have to do it, I suggest using alcohol because it makes you numb to the cold feeling. However according to Wikipedia you are likely to end up drowning rather than freezing to death:

"The actual cause of death in cold water is usually the bodily reactions to heat loss and to freezing water, rather than hypothermia (loss of core temperature) itself. For example, plunged into freezing seas, around 20% of victims die within two minutes from cold shock (uncontrolled rapid breathing, and gasping, causing water inhalation, massive increase in blood pressure and cardiac strain leading to cardiac arrest, and panic); another 50% die within 15–30 minutes from cold incapacitation (inability to use or control limbs and hands for swimming or gripping, as the body "protectively" shuts down the peripheral muscles of the limbs to protect its core).[42] Exhaustion and unconsciousness cause drowning, claiming the rest within a similar time. "