First, please read this article from the New York Times: http://travel.nytimes.com/2013/01/20/travel/has-snowboarding-lost-its-edge.html?_r=2& It's really interesting and informative. I promise.
We've known snowboarding's popularity has been dwindling for a while now. This article sums things up well, and attributes some factors to the decline.
I think both sports are almost the same thing now. The animosity between two-plankers and knuckle-draggers from the 90s is essentially gone. The big wave of snowboarders that started during that time are all in their late 20s or early 30s now and have better things to worry about. I ride with a lot of snowboarders and can share the same stoke for the sport with snowboarders. I go on trips with snowboarders and they do the same with skiers.
Given that, I think the two sports will thrive or survive in tandem. Whether it's a dismal economy or a loss of general interest, things don't look good for the future of the skiing and snowboarding industry. Of course, this doesn't mean that all of a sudden you won't be able to ski or snowboard. If it's still fun, keep doing it. A shrinking industry does mean that there will be less money being earned by resorts and you will see shorter ski seasons, and much smaller or diminished terrain parks.