The tourist season is fast becoming an all-year-round affair in Milan. For touring and good weather sports (such as golf, swimming, etc.) April to late October is the best.
For women: in summer, lightweight clothes including cottons for summer and light sweaters (evenings can be cool). Low-heeled shoes for sightseeing.
A cocktail or short evening dress might be useful.
When visiting churches (shorts are forbidden) wear hats or scarves on your head, stockings and preferably dresses with sleeves.
For men: in summer, lightweight suits, a light topcoat, slacks and sport jackets. Heavy clothes in winter.
Milan has continental climate, in the winter it is rainy or snowy. But the months from April to November are usually filled with warm sunny days; July and August normally are the hottest months of the year.
See the chart below, indicating maximum and minimum average temperatures in Milan and the cities around in degrees centigrade (oC).