Should I include opposing arguments in my exam essays?

This depends on how you wish to construct your argument.
One on hand, if you were asked "What factors enabled the improvement of the West German economy following the Second World War?", your argument would involve explaining and proving specific examples, so you would not necessarily need to include opposing arguments throughout your essay to do this. On the other hand, with questions that involve a statement, or a "to what extent..." proposition, arguments from elsewhere may help you to develop your discussion. For example:
‘Between the end of the Civil War and 1890, the position of African Americans in the United States significantly improved.’ Assess the validity of this view.
You may argue that this statement ignores wider economical and political obstacles that African Americans faced after emancipation such as poverty and KKK violence. As a result, you may wish to briefly quote an argument that agrees with this statement in order to highlight these interpretive flaws. To achieve the higher grades, students are required to evaluate different ways in which the past has been interpreted. It is therefore useful to include arguments where necessary to demonstrate how you believe your interpretation to be the correct one.