The issue of who started the Cold War would be more important than when it started. In addition, if you know who started it, you would also know when it started.
The issue of who started it is more important because it is an issue of causation rather than simply an issue of fact. What is interesting about history is not so much when things happen as it is why they happen. There is no thinking involved in understanding when something happened. But there is thinking involved in trying to understand the causes of some event. In addition, understanding causes of events can conceivably help us to avoid similar events in the future, while knowing when they happened is not nearly as likely to be useful.