The exact extent to which astrology played a role in the conduct of the Second World War is a topic that will probably never be fully realized, both because of the psychological desire on the part of astrologers and their followers to validate their beliefs through examples of historical application of astrology, and because of the desire on the part of public officials to refute the notion that they would allow themselves to be guided by such an inexact "science." Consequently, if astrology did in fact play a major, or even a minor, role in the decision-making processes of national leaders during the war, the facts may never be completely known.
What is known, however, is that some high-level officials in the Nazi Party were convinced of the validity of astrology, and did consult astrologers, most prominently Karl Ernst Krafft. What is also known is that British Intelligence was aware of this, and greatly exaggerated the importance of astrology to Adolf Hitler. In fact, the British consulted an supposed expert on astrology itself, Louis de Wohl, a Hungarian exile, in an effort at determining what kind of advice, based on astrology, the German leader was likely receiving. De Wohl, however, turned out be a fraud.
Another development that is is known for a fact is that the high-ranking German official who believed most fervently in astrology, Rudolf Hess, famously flew to Britain in May 1941 to discuss ways to end the fighting between the two countries, and that Hess's departure -- apparently a surprise to the Fuhrer -- both disgraced Hess in the eyes of Hitler, and delegitimized astrology in the latter's estimation.
Left unresolved is the record of Karl Krafft, whose prognostications remained eerily accurate. Krafft was an astrologer. Krafft also proved to have an amazing track record for predicting the evolution of the war. As the direction of the war turned against Germany, and as Krafft's predictions proved increasingly accurate, he lost favor with the German secret police and with his one-time benefactor, Joseph Goebbels, who had utilized the astrologer's predictions prior to the war -- when the Nazi Party was ascendent in German politics. Predictions of negative developments were well-known to be anathema to Hitler and his subordinates, who were frightened of presenting the Fuhrer with negative information. Krafft was arrested, for the second time, and imprisoned. He was scheduled to be transfered to Buchenwald concentration camp when he died.
In conclusion, while astrology may have played a role in the National Socialist Party's rise to power -- and that is uncertain -- it does not appear to have played an important role in the conduct of the war. Rudolf Hess's departure for Britain and the subsequent refutation of astrology occurred early in the war (May 1941, one month prior to the ill-fated invasion of Russia). It would be wrong, therefore, to suggest that astrology was a determinant in the evolution of the war.