I agree with Bob and Rich, if you are going to store them outside the house definitely store them in a climate control storage area. Especially if you have the early ones. Their paints are water based. The later ones can handle more climate abuse, but no one knows how much for sure.
I personally would keep the Styrofoam insert for the same reason, Bob stated. I also feel that keeping the Styrofoam insert is better for the secondary market. At this time the value difference probably would be insignificant but if I was in the market of buying a lets say a Thomas Point and there were two for sale for the same price. One had the insert and the other didn't, you know what one I would pick.

Now when it comes to peanuts it has always been acceptable to throw the peanuts away and fold the box to store it. In the future I feel that peanuts may even play a rule in the Harbour light collectablity. The style of peanuts has already changed and I don’t think they even make the same exact type as was packed in with the early HL’s. With prices of oil soaring, the peanut packing days may fall to some other sort of packing. Peanuts are all ready expensive for packing, and that alone would make it a good idea to keep them. If you can find the room.