The Cold War helped to bring about globalization because it helped to make various countries more important to one another. At the same time, it blocked globalization to some degree because it caused the world to be split into two blocs that generally did not have a great deal of contact with one another.
During the Cold War, various countries came to matter more to one another. This was because the superpowers wanted to get smaller countries of the world on their side so as to gain an advantage in their competition with one another. So, for example, it is likely that neither the Soviet Union nor the United States would have cared much about Vietnam had it not been for the Cold War. However, the Cold War competition made it so the superpowers cared very much about that country. The same was true of various other countries such as Angola or Afghanistan. Thus, the superpower competition led to more globalization as the superpowers tried to trade with smaller countries and/or give them aid so as to get those countries on their side.
However, the Cold War was also about dividing the world. The superpowers each created blocs of allies with whom they developed close ties. They generally did not want their allies to be having much in the way of contact with the other side. The Soviet Union did not, for example, want to encourage ties between Romania and the United Kingdom. This blocked globalization. It led to a situation where even countries as close to one another as Cuba and the US (or North and South Korea) did not trade with one another or have other sorts of contact.
In these ways, the Cold War both encouraged and blocked globalization.