I have had a side by side refrigerator in our garage for about two years and it is not hooked up to water. However, the dispenser area continues to be moist and is quite moldy.
You should be able to clean this with baking soda and salt mixture. Mix your baking soda with salt. Add a few drops of water to make a paste. Use an old toothbrush to scrub the mold off the unit.
I need to find out if there is any way to clean (instead of replace) the lines and water reservoir in my "Whirlpool" refrigerator icemaker/water unit.