The unlikely friendship was formed last year when President Dmitry Medvedev visited Silicon Valley and then sought the then-California governor's help in creating Russia's own version of the high-tech hub.
The tweets and planned skiing trip raise the possibility that Arnold Schwarzenegger may be looking at Russia as he ponders what to do with his time, and money, now that he has left the governor's office.
On Schwarzenegger's last day in office, Medvedev sent him a message on Twitter wishing him success and saying "there are many more interesting opportunities still to come."
Schwarzenegger tweeted back: "I hope you're having a great new year and can't wait to see you again - maybe skiing?"
Apparently they had already discussed the idea, because Medvedev responded by tweeting: "We agreed - I remember. We'll definitely find the time."
They will make an unusual pair on the slopes. The former Mr. Universe towers over the slightly built Medvedev, who stands just 5-foot-4.
But the two men, though nearly 20 years apart in age, appear to have found an easy rapport, sharing laughs and warm handshakes during their times together.
Schwarzenegger and Medvedev met in June when the Russian president visited California to see what he described as "the origins of success." Medvedev's high-tech tour began at Twitter's headquarters in San Francisco, where he set up his account and sent his first tweet.
They met again in October when Schwarzenegger brought a delegation of mostly California business leaders and venture capitalists to Russia to help them establish connections. Giving a further boost to Medvedev's project, Schwarzenegger declared during his visit that the potential for growth in Russia was so extraordinary "it's like looking at a gold mine."
Schwarzenegger said he was thrilled to be back in Moscow, which he first visited while starring as a Soviet anti-narcotics policeman in the 1988 blockbuster "Red Heat." He also reminisced about his teenage adoration for Soviet weightlifting champion Yuri Vlasov, who he said had inspired him to take up bodybuilding in the early 1960s.
His friendship with Medvedev was evident when the Russian president gave him a ride from his country residence to Skolkovo in a vintage Soviet limousine, a cream-colored Chaika designed in the 1950s.
It remains to be seen whether he is considering investing in Russia, where the realities of doing business can be daunting. Corruption is systemic, and the courts cannot be counted on to protect property rights.
But first he and Medvedev have a skiing trip to plan. They could choose Schwarzenegger's native Austria, though a more likely choice might be Sochi, the host city for the 2014 Winter Olympics. Medveded on Tuesday was already there.