In Roosevelt's Four Freedoms Speech (1941): If he had survived, do you think Roosevelt would have characterized the Cold War and Soviet Union the same way he did World War II and the threat of the Nazis? Why or why not?

This is a very interesting question! Roosevelt's vision of a new world order was based on four essential freedoms: freedom of speech and expression; freedom of religion; freedom from want; and freedom from fear. The first two were already enshrined in the US Constitution, and all four elements are contained within the Universal Declaration of Human Rights (1948). The threat of communism was in direct conflict with each of Roosevelt's four freedoms, particularly freedom of speech and expression. The most immediate freedom that was in jeopardy before the Cold War (which most historians recognize as having begun in 1946) was freedom from fear; according to Roosevelt:

Freedom from fear—which, translated into world terms, means a worldwide reduction of armaments to such a point and in such a thorough fashion that no nation will be in a position to commit an act of physical aggression against any neighbor—anywhere in the world.

While American experts had predicted the Soviet Union would not have nuclear weapons until the 1950s, there was still grave concern over Russia amassing nuclear weaponry in Roosevelt's time, as evidenced by his speech. Months after Roosevelt died, the end of the Second World War left America and the Soviet Union the two dominant world powers. If communist influence spread, no coalition of nations would be able to defeat it. In 1950, months after the first Soviet bomb was detonated in 1949, National Security Council 68 concluded that the Soviets would manufacture more weapons, including nuclear, and that the best course of action was to respond with a similar amassing of weaponry. President Franklin Roosevelt was the only President to serve more than two terms (he served four). If Roosevelt had lived, and the 22nd Amendment of the Constitution had not been passed in 1947, let us assume that Roosevelt would have supported the conclusions of NSC-68 as Truman had.
One passage in Roosevelt's speech is directly relevant to the Nazi regime:

A revolution which goes on steadily, quietly adjusting itself to changing conditions—without the concentration camp or the quick-lime in the ditch.

Note that the US was not fully aware of the horrific circumstances of the Holocaust until American soldiers began to liberate the camps (after Roosevelt's death). The US did not get involved in the Second World War because of the Holocaust, and liberating the Jews was not a priority (as opposed to defeating the Nazis and retaliating against Japan after Pearl Harbor). As such, I do not think Roosevelt was thinking of mass murder in his speech; until the time leading up to the end of the war and the subsequent Nuremberg Trials in 1945 and 1946, this scale of mass murder was viewed as inconceivable. Moreover, I would assume that Roosevelt would have included this in his speech had he been aware of the true circumstances.
So, given Roosevelt outlasted the Nuremberg trials and went on to win a fifth term, I would say that he would have recognized the potential for the Soviet Union, given its influence's spread, to proceed as the Nazi regime had, given crucial similarities. According to A. James Gregor, Professor of Political Science Emeritus at the University of California, Berkeley:

Stalin had created a regime that had abandoned every principle that had presumably typified left-wing aspirations and had given himself over to notions of “socialism in one country”—with all the attendant attributes: nationalism, the leadership principle, anti-liberalism, anti-individualism, communitarianism, hierarchical rule, missionary zeal, the employment of violence to assure national purpose, and anti-Semitism—making the Soviet Union unmistakenly “a cousin to the German National Socialism.”

To focus on anti-Semitism: after the foundation of Israel in May 1948, despite his personal dislike of Jews, Stalin had been an early supporter of a Jewish state in Palestine. However, Stalin became increasingly afraid of pro-Israeli feeling among Soviet Jews, which he believed subverted the Soviet regime's influence. Whether these circumstances would have gone on to trigger a second genocide akin to the Holocaust will never be known, but the potential was there.