I don't store my ponies in cardboard boxes, and here's why:
1) Cockroaches are attracted to cardboard. Any type of bug or creature can get into the cardboard box and damage the ponies in a multitude of ways.
Worse yet: If you have them in your area, Brown Recluse spiders love hiding inside or in between cardboard boxes because it simulates tree bark to them or something. That's why I've been eliminating boxes as storage in my house because they're here. I'm replacing them with plastic stacking containers I buy from where I work.
Yeah, and I don't even want to mention mice... but they love cardboard and will get to whatever is inside the cardboard, too.