This was inspired by the story of Samantha Smith, a little girl from Maine who, in 1983, wrote a letter to then-Soviet Premier Yuri Andropov about her concerns over nuclear war. She was invited to the USSR to speak to the Premier. Smith later starred in a series called Lime Street (1985), which stopped production because of her death in a plane crash. Coincidentally, the show aired on ABC directly opposite "The Golden Girls."
In real life, the lead actresses were animal lovers and activists who were against real fur coats, so they wore fake fur coats during Rose's dream sequence. After Rose wakes up from the dream, she mentions how they were wearing fake furs, so it's emphasized to the audience as well.
Sophia's remark in Rose's dream about getting a ride to Moscow with a German guy with a plane is a reference to Mathias Rust, who in 1987 flew a light aircraft from Helsinki, Finland to Moscow and landed near Red Square. He intended it to be a mission of peace, but it only sparked consternation among members of Russia's air defense, many of whom faced serious consequences.
Blanche singing Happy Birthday to Mikhail Gorbachev is based on Marilyn Monroe's famous rendition of the song to John F. Kennedy.
Sophia makes a joke about how Valerie Harper was entertaining the masses and then got cut from show business. It was a reference to Harper playing the title role in the television sitcom Valerie (1986), only to get fired after the first season, and then the show was re-titled into "The Hogan Family" with Sandy Duncan being Harper's replacement.