Indicate a period or artist that has had a significant impact on the political development of the culture.
The Renaissance seems like a relavant answer to your question. The arts experienced a resurgence as did science and philisophy. Culture took center stage and this vital energy translated into politics, eventually leading to the installation of democracy in the US and France.
Perhaps this is too tenuous a connection, drawing the 17th and 18th centuries together, but it seems possible to draw a line between Rembrant and Jefferson if the line is one of awakened sensitivity to man's spiritual state.
Norman Rockwell is certainly not an "artist" in the same sense as Picasso (or even Warhol), but he was an immensely popular painter and illustrator during his time and had a knack for capturing (and even sometimes influencing) the public mood, particularly in his widely circulated magazine covers. The paintings in his series called The Four Freedoms are still widely known, as is much of his work, including work he did to promote the war effort during World War II. It would be very interesting to examine the political beliefs and influence of Rockwell. A Google Books search for "Norman Rockwell politics" would be a good place to begin.
Andy Warhol (August 6, 1928 to February 22, 1987) was a significant influence on Pop Art and Pop Culture. Warhol's work precipitated reexamination of artistic and cultural values as evidenced by the 1962 Symposium on pop art orchestrated by New York's Museum of Modern Art. This reexamination undergirded, as well as spurred, and was coincident with a general reexamination of moral, spiritual and political values that occurred in the 1960s and continued through the 1970s, with its greatest expression being Civil Rights protests and protests against the Vietnam War.
Although I'm not sure of the names of the artists who created these pieces, I will tell you the most striking portrayals of the same event from very different political perspectives that I have seen with my own eyes.
In regards to the Pilgrims landing at Plymouth in 1620, think of how many times we have seen (in the United States) the picture of the battered Mayflower with it's sea-torn Pilgrims in black/brown and white happily landing at Plymouth Rock and thanking God for their safe passage. It is a very common and iconic image in the United States, and one that we cannot escape come Thanksgiving in late November.
The above image in itself, having grown up with it, has never struck me as amazing, ... but when I visited Parliament in London, England, I found the same event portrayed with a different image, indeed! As we toured the building, I stopped and smiled when I found a huge mural depicting that voyage in 1620; however, the focus wasn't on the landing at Plymouth, ... the focus was on the Mayflower leaving London, England in order to discover new lands! The focus, then, was on England's power enough to send its citizens to the wilderness of the world in order to settle & civilize!
An incredibly different political perspective, ... and one that will stick with me forever!
I don't know if you are referring specifically to visual artists in your question - the responses so far are all trending in that direction, but music is also an art form that has influenced cultures and politics tremendously over the years. Consider the music of Pete Seeger, Bob Dylan, Joan Baez - just to name a few American musicians from "my" era!
During the Renaissance, there was a shift from focus on religious figures to depiction of everyday life. This was revolutionary, because it demonstrated an emancipation from the church. Before that, the church controlled much of people's lives. It was a demonstration of independence.
One might also consider Massacre at Chios which gives a horrid depiction of the abuses committed by Turkish troops against Greeks during an uprising on the island of Chios. It is perhaps the second most famous of Delacroix's paintings, after Liberty Leading the People, an obvious political commentary on the French Revolution.
Certainly Picasso's Guernica is perhaps one of the most famous examples of a political painting in its presentation of the horror of the Spanish Civil War. I must admit, I can't think of many other artists whose works had a distinctly political element that was actually influential. The work of so many artists is often focused internally, such as Frida Kahlo and the various depictions of women and gender that are presented in her paintings. Picasso is a great example because his work commented directly on political realities of his time and had influence.
Pablo Picasso is a twentieth century artist who painted several anti-war paintings, such as Guernica in 1937, which is a violent condemnation of the indiscrimate massacre of Basques from an aerial terror attack during the Spanish Civil War, and Massacre in Korea, 1957, which is a criticism of American intervention. Another painting, Charnel-house, precipitated by the horrific revelation of the Nazi concentration camps of Buchenwal, Belsen, Dachau, and their multitudes of wasted corpses.
Although many of his paintings were very expressionistic and clearly anti-war, he was always neutral physically, having never served in any war. Picasso was at one time a member of the French Communist party. After Picasso painted Stalin, the party criticized the painting for being insuffienciently realistic; this criticism cooled some of Picasso's enthusiasm for communism. Nevertheless, Picasso's communism has long been the subject of much controversy.