OK, compared with most of you people my stock is quite basic. However, I bought an inexpensive (some might say cheap and cheerful) brown plastic storage box. It has plastic sides, bottom and top which seem to provide a water-proof area for my limited stock. In addition I have hung wooden shelves to increase my storage space.
Last time I looked there was no sign of any water ingress but I will check again later today.
My controllers and locomotives are stored at the bottom of my wardrobe for safety. Unless I leave a locomotive in the kitchen for ease of access if the weather is good enough to enjoy a train.
I did consider insulating the box but I wonder if it is really worth it?
If you can get any Plastic Decking will survive any weather conditions but may need support due to sagging. I find that a bit of shelving cut depth of shelves in middle should work fine. Wicks certainly have Plastik Decking if you have one near you, though Wooden Deck (most DIY Sheds) inside your Box should work just as well.
I stored my rolling stock outdoors in a similar box in Maryland for many years. (-5C to 35C). Didn't see any problems, except for the bugs - spiders in particular liked to build little nests in the cars. I would not store cardboard boxes or similar outside in a damp environment.