This is something of a difficult question to answer because there are many ways to answer it.
First, we could say that the Cold War involved the United States and the Soviet Union. These were the two superpowers in the world during the Cold War and they were the main players in the Cold War. The Soviet Union was trying to spread communism and the US was trying to prevent that spread and to promote democracy and capitalism.
Second, we could say that the US, the USSR, and a few other countries were mainly involved in the Cold War. These other countries could include China, the two Koreas, the two Vietnams (there were two up until 1975), and a few others. These are the countries that were most affected by the Cold War. There were wars fought in Korea and Vietnam. The Chinese participated to some degree in both of those wars. Therefore, countries like this were involved as well.
Finally, we could say that essentially every country in the world was involved in the Cold War. The Cold War dominated the world scene to the extent that all countries had to take sides in some way. All of them were affected by the competition between the two superpowers.
Thus, we can answer this question in a number of ways, depending on how we define “involved.”