PLT OF COMMERCIAL CHK RIDE INSTRUCTED BY EXAMINER TO TAXI ON SNOW COVERED TXWY HAS NOSEWHEEL STICK IN MUD AND PROP STRIKE GND.

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I WAS IN THE MIDDLE OF MY COMMERCIAL PLT CHK RIDE. I WAS IN FBO'S SMA. WITH ME ON BOARD THE AIRPLANE WAS AN FAA DESIGNATED EXAMINER. THE EXAMINER INSTRUCTED ME TO PERFORM A SOFT FIELD LNDG INTO BRIGHTON ARPT. UNDER NORMAL CIRCUMSTANCES I PERSONALLY WOULD NOT GO INTO THIS ARPT DUE TO SAFETY REASONS. THE REASONS BEING; THAT THE RWY IS VERY NARROW AND MUCH OF THE FIELD IS UNIMPROVED. THE EXAMINER EXPECTED ME TO FOLLOW HIS INSTRUCTIONS SO; I ATTEMPTED THE LNDG INTO BRIGHTON FIELD. THE AIRPLANE LANDED HALF WAY DOWN THE RWY AND I KNEW WE HAD TO TAXI BACK TO THE BEGINNING OF THE RWY FOR TKOF OUT OF THE FIELD. THE WIDTH OF THE RWY RULED OUT DOING A 180 DEG TURN AND BACK TAXIING DOWN THE RWY. THE EXAMINER THEN POINTED OUT A TURN OFF THAT LED TO A PARALLEL TXWY. HE INSTRUCTED ME TO TURN OFF THERE. AS I TURNED OFF WE INSPECTED THE TXWY. SNOW COVERED HALF OF THE TXWY AND THE OTHER HALF WAS PLOWED. THE EXAMINER SAID IT WAS ODD THAT THE ENTIRE TXWY WAS NOT PLOWED. HE ALSO TOLD ME THAT THE WHOLE LENGTH OF THE TXWY WAS PAVED. SINCE THIS EXAMINER HAS BEEN TO THIS ARPT MANY TIMES I BELIEVED WHAT HE SAID AND ASSUMED THE ENTIRE LENGTH OF THE TXWY TO BE PAVED. THE EXAMINER INSTRUCTED ME TO TAXI DOWN THIS TXWY. AS WE APCHED THE SNOW THERE WAS NO EVIDENCE THAT IT WAS NOT PAVED UNDERNEATH. ALSO THERE WERE NO ARPT SIGNS INDICATING ANY DANGER; SO I FOLLOWED THE EXAMINER'S INSTRUCTIONS AND TAXIED INTO THE SNOW. RIGHT BEFORE WE HIT THE SNOW THE EXAMINER TOLD ME 'JUST DON'T STOP.' AS WE HIT THE SNOW THE NOSEWHEEL SUNK INTO MUD; THE PROP HIT THE GND AND THE ENG KEPT TURNING. THE MIXTURE WAS PULLED AND THE ENG SHUT DOWN. THE EXAMINER AND I GOT OUT OF THE AIRPLANE UNINJURED; INSPECTED THE DAMAGE.