I read an article in Popular Mechanics a while back about the Mythbusters building a boat out of frozen newspapers based on a British WW2 plan to build aircraft carriers out of the same material (for the north atlantic of course...). If you can solve the issue of keeping said boat cold, it would solve the fundamental problem of waterproofing cardboard. I don't know how effective frozen cardboard would be as a building material however.
I found the article
here.