FAR 135 FLT WAS DIVERTED TO REMOTE STRIP TO PICK UP ADDITIONAL PASSENGERS. THE DISPATCHER WAS NOT AWARE THAT THE RUNWAY WAS COVERED BY 4 FT OF SNOW UNTIL THE ACFT WAS BEYOND RADIO RANGE. THE PLT ASSUMED THAT THE RWY HAD BEEN PLOWED AS IT WAS IN PREVIOUS WINTERS. THE BOX CANYON CONDITION OF THE SURROUNDING TERRAIN PRECLUDED THE PLT FROM OVER FLYING THE RWY TO CHECK ITS CONDITION. ON APPROACH THE RWY APPEARED TO BE A NORMAL SNOW PACKED SURFACE. THE PLT LANDED THE AMPHIB FLOAT ACFT WITH THE LANDING GEAR DOWN AND THE AIRPLANE NOSED OVER DURING THE LANDING.