THE STUDENT & INSTRUCTOR PLT (CFI) WERE ON A DUAL X-COUNTRY FLT. THEY PROCEEDED TO FLY TO AN UNATTENDED ARPT AT EMIGRANT GAP, CA, WHICH WAS AT AN ELEVATION OF 5284 FT. AFTER ARRIVING, THEY CIRCLED THE ARPT & MADE A LOW PASS OVER THE RWY. THEY SAW TRACKS ON THE RWY & ASSUMED THAT ACFT HAD BEEN OPERATING FROM THE ARPT. (LATER, THEY LEARNED THAT THE TRACKS HAD BEEN MADE BY SNOW MOBILE TYPE VEHICLES.) THE CFI ASKED THE STUDENT TO MAKE A SOFT FIELD APCH & LANDING, THEN IMMEDIATELY GO AROUND WITHOUT LOWERING THE NOSE. HOWEVER, WHEN THE MAIN GEAR TOUCHED DOWN, THE WET, UNPACKED SNOW CREATED SUFFICIENT DRAG TO CAUSE THE NOSE TO DROP. SUBSEQUENTLY, THE NOSE GEAR COLLAPSED & THE ACFT NOSED OVER. THE ARPT/FACILITY DIRECTORY STATED THAT THE ARPT WAS UNATTENDED & WAS CLOSED IN WINTER. THE INSTRUCTOR HAD NOT CHECKED THIS DIRECTORY, BUT HAD CHECKED 2 PRIVATE PUBLICATIONS.