Yeah I'm with Dictamnus on this one - 99% of the people I've seen who do Supernatural costumes just use plain black feathered wings. Purchased as well as hand-made with regular feather-wing tutorials.
But if you want the transparent look of those? Cardboard is not what you want anyway. Even if you were making solid wings, I would not go cardboard as my first, second, or even third choice. I know it's cheap or free in some cases but if you want genuine 4-foot long wings (for an 8 foot wingspan?) you need something that will be lightweight and you're already going to need to work out a harness to mount them on, so take a step back here and decide your parameters. Do you already have the harness thought out? Do you know how the wings will need to fold or break down for storage and transportation? Do you want them articulated or static? If you haven't solved these problems yet, finding a large enough cardboard box is the least of your worries.
If you want them translucent, you're looking at a sheer fabric - chiffon, gauze, or netting, likely mounted on wire that is both strong enough to hold it up and lightweight enough not to weigh 20 pounds on your back. If you want them feathered, that's a whole different method entirely. If you just want them to look like a generic wing-shaped thing, I would still go fabric sheath over anything solid like cardboard. Because while some people have been able to work miracles with it, I don't know about you, but when I cut out a giant piece of cardboard and paint it, it looks exactly like painted cardboard and not at all like what it shoudl be.
Founder and President, Madison Area Costuming Society, a chapter of the International Costumer's Guild
Strange Land Costuming - www.strangelandcostumes.com