Once EPCOT opened in 1982, people wanted thrills and such in this (what some said) boring park, about learning. Beginning a couple years after the opening of EPCOT rumors started swirling of mountains being built around the world showcase. THe first rumor was shown in pics from the area, a Mount Fuji attraction located in the Japan pavilion, along with that rumor was the one about the Tokyo Disneyland attraction, Meet the World and the simulator bullet train ride through Tokyo Underground. The Mt. Fuji attraction would have been a copy of the Matterhorn Bobsleds, without a Abominable Snowman. THe mount Fuji concept has yet to be dropped, still there are rumors every-so-often that it will be built. But conflicts to find a sponsor are a problem. Also, Kodak, the sponsor of the Imagination pavilion would not be happy to hear that an attraction with Fuji in the name, their rival company, in the same park they are sponsoring an attraction in.
A few years later a rumored and conceptualized pavilion of Switzerland was in development. And it was planned to have a Matterhorn type attraction in the pavilion. The Walt Disney Imagineers looked for Swiss sponsors for the pavilion, but never found one willing enough to sponsor.
Around the mid 1980s along with the rumors swirling of the mountains coming to EPCOT, there was also a rumor and concept of the Matterhorn in the new Disney MGM Studios park. You say to your self, how does a Swiss snowcovered mountain fit into the hollywood backlot theme? Well, it seems that it would have been themed to a movie set with just the back side, towards the road, fully completed. The idea behind this version of the "Matterhorn" was that WDW guests would get a big thrill out of seeing how close their ride vehicle was actually coming to the "mountain"'s support beams. Which would have added to the fun of this Disney-MGM Studios thrill ride.
Years later around the 1990s, the rumors didnt stop. People said that not just one of the mountains would be built, but both. Creating a mountain range in the WOrld Showcase, creating two seperate wienies in the two opposite ends of the World Showcase. Some said they would be visual book ends to the American Adventure pavilion. THen in the late 90s when talks were happening about the new Animal themed park, which would have featured a mystical themed land with mythological creatures, one being the Abominable Snowman. THen once the land was never built rumors started up again for Matterhorn and/or Mt. Fuji attractions in Epcot's World Showcase.
In the mid 1990s, rumors once again started to swirl around the mountain being added to Magic Kingdom, again. But, in a different theme, either in a volcano called Fire Mountain for Adventureland or Dark/ Villians Mountain, in Fantasyland. Those rumors were swirled for a while, but were never as strong as the mountains of Epcot rumors.
Finally, in 2003 the rumors came true, but in a whole new form. During the 2003 Disney's Animal Kingdom 5th Anniversary Press Conference it was confirmed and announced that the Forbidden Mountain was coming to Asia, in Disney's Animal Kingdom.