Nature's Wonderland (including the Rainbow Caverns) was a classic Disneyland attraction which was closed to make room for the more thrilling Big Thunder Mountain.
Mickey's comment about someone building a "big, thundering mountain" where the Rainbow Caverns were meant to be alludes to the fact that the Big Thunder Mountain ride at Disneyland replaced the Mine Train Through Nature's Wonderland.
Mickey's souvenir map is an accurate map of the Mine Train Through Nature's Wonderland attraction upon which the cartoon is based.
Mickey exchanges a wink with an illustration of Walt Disney on his map.
Mickey's song is set to the tune of "Little Wooden Head" from 'Pinocchio,' a melody which was briefly quoted in the introduction to "When You Wish Upon a Star."