Those are awesome. I have some similar crates in my sewing room, but they're the cheap white ones from Home Depot and aren't nearly as pretty as yours.
You have to watch storing things for a long period of time in cedar chests. Cedar wood has oil (which is what keeps the bugs away) and that oil can seep onto whatever is stored in it. My mother always said to wrap things in sheets before putting them in the chest and I've always done that. I wasn't until a few years ago that I learned that that is the best way to store textiles in cedar.