Yes, those divided ornament tubs are wonderful! I still wrap some of my more precious ornaments in tissue before I put them in the tub, though.
My nativity scene is individually wrapped and placed in a sturdy, well-marked tub, too. In fact, all my Christmas decorations are in tubs. I keep them in the garage which is somewhat insulated, and they've done fine over the years as far as I can tell. Oh, except for the year I stored my candles in a tub too, and the tapers softened and bent a bit! I have four boxes or ornaments, and several large tubs of other decorations. There's just not room for them in the house.