If you line the cedar chest with muslin, it would be okay. Alternatively, place quilts inside pillowcases. Cedar chests, as is the case with all wood products (cardboard, tissue paper, etc.), leaks an acid that will gradually eat fabric. Many vintage quilts that were stored unprotected in cedar chests come out with "rust" lines along the folds where the fabric touched the wood; that is the beginning of the acid damage.
If you encase your quilts in pillowcases and take them out every year or so to wash the pillowcases (and refold the quilts along different lines), you would be okay.