Why? To make room in your closet so that everything isn’t crushed together, and because seldom-used clothing that sits neglected in the back of your closet, never seeing the light of day (literally), is the perfect breeding ground for clothing-eaters.
Holes in sweaters, in this country, are more likely to come from carpet beetles than clothes moths (carpets being historically made from wool), and actually the larvae of the carpet beetles. Carpet beetles will eat any animal fibers (wool, silk, suede, fur, feathers) as well as synthetic and plant-based materials (polyester, cotton) that are heavily soiled. And they are particularly attracted to undisturbed clothing, so anything to be stored over the summer (think warm, humid, and dark) should have proper precautions taken.
So what? So many of the remedies for moths will not affect carpet beetles. This is a two-pronged attack: kill any existing eggs that have been laid, and then repel any further insects from laying eggs.
Kill: Clean everything. There’s a good chance that there are eggs on your stuff right now, and any food particles, stains, body oils, or dead skin on the coat will attract carpet beetles in storage. Take it to be dry-cleaned (or preferably wet-cleaned) or put it in the washing machine depending on the care instructions. Dry cleaning kills eggs, as does washing with hot water. If something can’t be washed in hot water, wash it cold, and then, once it’s completely dry, put it in the dryer on high for about half an hour.
What about the coat you never even wore this winter? That means it’s probably been a perfect environment for beetles to lay eggs, because it’s been sitting undisturbed in your closet. I suggest dry-cleaning it anyway. If you’re that cranky about it, you can take it out into bright sunshine and brush it with a hard-bristled brush, getting into all the crevices and seams. And think about getting rid of the coat, or keeping it in deep storage.
Repel: Most natural-chemical repellants, like cedar or lavender, only work against moths and not carpet beetles. Mothballs are poisonous, smell horrible, react badly with plastic, and only work in a very airtight enclosed space. You could put your clothing in an airtight plastic container, but any moisture left on the clothing will condense and create mildew. I suggest using breathable containers, like garment bags or boxes, made from clean cotton (which carpet beetles do not eat), and wrapping the coats in layers of clean cotton.
Coats can be folded in boxes or hung on padded, heavy-duty hangers. Stuff any areas that you don’t want crushed, like the shoulders, with tissue paper.
For fur: Fur needs special attention. A fur coat should be sent to a specialist for cold storage. Any fur trim is ideally detachable, and should be sent to cold storage, as well.