I would probably donate them, but I would want the museum or historical society that took them to have a good textile storage facility and good textile preservation practices. Good archival storage for quilts is not common among museums. I think the ideal is for the quilts to be stored flat, between layers of sheets or achival quality paper, in temperature and humidity controlled rooms. They should also be handled only with white gloves.
Regarding the cedar chest, you would be well advised to remove them immediately because wood contains acids that first stain and then eat away at fabrics. Many old quilts are stained by acid along the fold lines from storage in cedar chests for years at a time. A good way to temporarily store quilts is to lay them on top of each other on a bed, with a sheet between each one. Ideally you want the bed big enough so the edges don't hang over, but edges hanging over would be preferable to storage in a cedar chest or in contact with any other wood product (such as tissue paper that is not archival quality -- i.e., processed to remove the acid).
Before donating, I would write as much information as possible about the quilt, the person who made the quilts, and include any pictures of the person and the family from that time.