I know exactly how you feel. It is how the back of my closets are. If you look I have posted a entry in mold prevention. It list ways to help. It's rather long but if you can take a look under tips; I really feel it would help you out. This can do damage to your clothes so you must address the problem. There are inexpensive ways as well as things you can purchase to help.
One of these is as listed keep it open,or cracked a little. In my home it isn't just in the closets but that moisture causes mildew, damage you may not be aware of. Sorry I couldn't just rewrite it all here but please go look at the current tips, I think its the last one (or first posted). I know it will help. Good luck, God bless!
What I believe is happening is warm moist air in getting into the closet and coming in contact with the cold walls and other cold areas and forming water droplets. You can see the same effect when you have a glass filled with a liquid and ice cubes on a warm summer day. Water droplets form on the cold exterior of the glass. You could leave the closet door open or maybe turned on light bulb in the closet would have enough heat to warm the air to prevent the condensation from forming.
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