I've no idea how much of a PitA this would be, but I'm guessing, since most newspapers' profit (if they make one) is based on advertising revenue and not the "newsstand" price of the paper itself, a lot of local papers would probably be happy to give WDW all the papers they need, for free, just to be able to claim to their advertisers that THAT many more eyeballs are seeing their ads. Same way Coke supposedly gives their syrup away as part of their advertising deal within The World.
Furthermore, if WDW were really concerned about going green, they could even audit the amount of papers they need. Upon check-in, they can ask you if you want a paper, they can tally the yes-es, and the local paper of record could possibly adjust the amount of copies they generate to accommodate the amount of copies they need, plus gladly leave a few dozen out in the lobby of each resort for anyone who wants one. They could even add an additional sticker from an advertiser - This Free Copy of the Orlando Sentinel Courtesy of Florida's Natural Oranges" or whoever winds up eating the costs, and only the amount of trees necessary to murder to get the amount of copies guests want get killed.
But ultimately, it's a moot point. Because WDW doesn't want to afford people the option of reading the newspaper. Because if you're reading a newspaper, you might see an ad for a sale in one of the outlet malls or a restaurant a short cab ride away, and that's time you're not spent at Disney potentially buying Disney stuff. USA Today wouldn't be so bad because there's not as much local advertising in it, but nonetheless, Disney only wants you looking at THEIR ads.
Heh, what would be interesting is a WDW-centric version of a sort of mini USA Today, where Disney gets the layout sent to them digitally, and they are allowed to insert the advertising they choose to insert, for distribution only on WDW grounds. Of course, then you run the risk of them exercising editorial control, choosing happy stories they want you to read and censoring stories of the politician-gone-astray or pretty-girl-gone-missing-presumed-dead variety.
Bottom line, newspapers in Disney probably won't happen. You're better off wishing for free wifi, which will be a moot point anyway soon, the way most people are gobbling up smartphones you won't need wifi.