The pilot reported that following an uneventful takeoff in the amphibious float equipped airplane, he intended on performing a water landing at a nearby lake as part of his checkride. During the water landing, the airplane immediately nosed over which resulted in substantial damage to the fuselage and wings. The pilot stated that he had become distracted after takeoff and did not retract the landing gear for the water landing. The designated pilot examiner onboard the airplane, reported that he did not confirm the position of the landing gear prior to the water landing. The pilot reported no preimpact mechanical malfunctions or failures with the airplane that would have precluded normal operation.