March is the start to the end of the rainy season in Peru, but you can still expect to have a fair number of wet days. At that time of year you could expect mostly dry mornings with more clouds and rain in the afternoon/evening. Arequipa will be drier than Cuzco, and the climate in Lima should actually be rather nice. They get a lot of sun along the coast that time of year - the rains are mostly confined to higher elevations. Don't let the threat of rain keep you away.