In this specific meme, Putin rides an american buffalo. An american icon indeed. Buffalos have been part of the New World's folkore since the Conquest of North America's West and expressed that national identity many times(1). This may mean an undercover critic to Putin's relative freedom to comply with UN decisions.
(1). President John F. Kennedy's Inaugural Parade. January 20, 1961. 2'50''
The series of memes "Putin rides" takes an image appeared in August, 2007 as its starting point. This image belongs to a set of photos shot during the president's summer holidays in Jakasia Republic. The photos were taken by Putin's personal photographer, part of his personal assistance team that's accompanying the president daily .
The coverage of Putin's personal life is obviously a modeling of the president's public image and part of Putin's social acceptance sharp planning, however endlessly disclaimed by his spokesmen.
Putin took russian presidency in year 2000 and there are expectations of him to keep in charge till ear 2025. He suddenly appeared on the political scene as the average russian man in clear opposition to Yeltsin's (his predecessor) degraded image. The media the party is publishing is suspicious of associating the traditional leadership values according to a patriarchal totalitarian power structure and supporting the very unhealthy relation between political power and religion in Russia.
Root image for the later reconfigurations shows naked chest Putin riding a horse, an attitude clearly connected to dominance, patriarchy, ability,... even to freudian sexual theories of admiration, how to make an icon out of a man. All this symbolism is actually understood by the online community and subverted as the series parodies these attributes transforming Putin into a kind of outlaw, a man above good and evil, that can do his will no matter what it is.
"Putin as Celebrity and Cultural Icon" Helena Goscilo, Routledge. 2012