AFTER LANDING, THE FLT CREW INITIATED A 135 DEG TURN OFF OF THE RWY & ONTO A TWY. ACCORDING TO FDR DATA, THE TURN WAS INITIATED AT 38 KIAS. THE CAPT RPRTD THAT THE NOSEWHEEL STEERING BECAME UNRESPONSIVE ABOUT 2/3 OF THE WAY THRU THE TURN. THE NOSEWHEEL WENT OFF THE TWY & INTO DEEP MUD. NO PROBLEMS WERE FOUND WITH THE NOSEWHEEL STEERING OR BRAKES.