B737 CREW RPTS RWY CTRLINE LIGHTS BURIED IN SNOW DURING CAT III APCHS AT DEN.

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CAT III APCHS ASSUMES NOT ONLY ONBOARD EQUIP IS WORKING; BUT ALSO THE LNDG RWY HAS ALL THE REQUIRED ELECTRONIC AND APCH/RWY LIGHTING. WHEN WE LANDED AT DEN EVERYTHING WAS IN WORKING ORDER WITH 1 MAJOR CAVEAT. SNOW WAS COVERING THE RWY CTRLINE LIGHTS AND MADE THEM UNUSABLE. WE HAD THE APCH LIGHTS WELL OUT ON FINAL (I WOULD ESTIMATE FORWARD VISIBILITY AT CAT I RANGES) BUT WE ARE LOOKING AT A COMPLETELY WHITE PICTURE SO THE RWY IS NOT VERY DISTINCT. ON SHORT FINAL I PICKED UP THE RWY EDGE LIGHTS AND GOT SOMEWHAT DISORIENTED BECAUSE I THOUGHT THEY WERE THE RWY CTRLINE AS I'M TRAINED TO LOOK FOR. THE DISORIENTATION WAS COMPOUNDED BECAUSE WE HAD AN 8 KT XWIND FROM THE L AND AS WE GOT CLOSER IN; THE LIGHTS IN FRONT WERE THOSE R EDGE LIGHTS WHICH LEAD ME TO BELIEVE THAT SOMEHOW I WENT FROM ON COURSE TO L OF COURSE. IT PROBABLY WOULD HAVE BEEN EASIER IF THIS WAS A NIGHT APCH BECAUSE THE RWY CTRLINE MIGHT HAVE BEEN VISIBLE THROUGH THE SNOW. A QUICK DISCUSSION WITH THE FO CONFIRMED WE WERE CORRECT AND I LANDED THE ACFT. SIMPLY PUT: ARE WE LEGAL TO LAND FROM A HUD CAT III APCH IF A PORTION OF REQUIRED RWY LIGHTING IS AVAILABLE BUT NOT USABLE? THIS IS A SAFETY CONCERN. ARE CAT III APCHS AUTH IF RWY CTRLINES ARE COVERED WITH SNOW AND ARE UNUSABLE?