Conduction is the method of energy transfer between two objects that are in direct contact with each other and have temperature difference. here, energy transfer occurs from warmer to the cooler object.
In the given condition, hand and glass of ice water are in direct contact with each other. The hand is warmer while the glass of ice water is cooler. Hence, energy will flow from hand to the glass through conduction.
I'm not certain on the reason it happens, but it can be lethal by stopping the heart from beating and, the lungs from contracting and expanding causing death by suffocation or cardiac arrest, also putting the body into shock.
