You can't find anything to numb the shock you'll first get? When you first fall into the water, your body will go into shock for 1-3 minutes. You'll start to hyperventilate and you will feel an intense sensation that engulfs you.
During the first minute of immersion in very cold water the body undergoes a massive reflex reaction. This is characterized by an uncontrollable gasping for breath, disorientation, and impaired coordination - all factors which may render a person incapable of swimming effectively and so lead to drowning. Sudden drop in external temperature upon entering dangerously cold water, blood is pulled away from the skin and shunted it to center of the body in an effort to maintain core temperature. This rush of cold blood to the heart may cause cardiac arrest. My point is your survival instinct might engage the fight or flight mode and you effectively would take longer than you think would happen for death. Maybe tie you're feet to a boulder and/or tie your hands together cause you'll initially fight it at first. If you could find anything to help fight the survival instinct it would help ease the pain especially when you start gurgling in cold water before you drown.