Nearing the conclusion of the instrument flight rules flight, the pilot of the multi-engine airplane was provided with radar vectors for an instrument approach in instrument meteorological conditions. During the decent, he observed an area of patchy fog over the approach end of the runway and leveled off to avoid the fog. He landed the airplane with about 3,000 ft of the nearly 6,000-ft-long runway remaining and felt the airplane hydroplaning while using a combination of wheel braking and the beta range of the propellers. The airplane subsequently overran the end of the runway, onto the adjacent grass and mud, collapsing the nose landing gear and impacting terrain. The airplane sustained substantial damage to the forward fuselage. The pilot reported that there were no preaccident mechanical failures or malfunctions with the airplane that would have precluded normal operation.The airport's automated weather observation station reported that, about that about the time of accident, the wind was from 270° at 3 knots, ½ statute mile visibility with fog and an overcast ceiling at 300 ft. The pilot was landing the airplane on runway 23.