Craft foam should work just fine to make the shoulder pieces (then you could add the details with more craft foam, hot glue, wire, etc. You have a variety of materials to choose from for that). I would be wary of using cardboard since it can't make those nice curves as easily.
The rain problem is an issue most cosplayers have
I think we tend to just count on events being indoors or not raining (you can always change inside the convention bathroom/hotel or bring a poncho or tarp to put over yourself to get inside). But if it's an entirely outdoor event I'm not sure if there is a good solution