The water line can freeze only where it has close proximity to freezer air. Chances are it is freezing behind the freezer door, about 4 inches into your dispenser. First, fix the freezing problem. You have a defrost problem most likely, so check both the defrost heater and defrost thermostat. I would replace the DT even if you are seeing it as okay. Replace the thermistors on the coil and in the freezer. Finally, install insulation on the inside of the freezer door just behind the dispensing unit. That wall is thin and your water line is freezing because the freezer is too cold for too long.