Trieste enjoys a fairly mild Mediterranean climate and basically there are two types of seasons in Trieste, i.e. summer and winter.
Summer (May to August): Trieste's summers are warm to moderately hot and dry. Most of the visitors choose to come in this good season to Trieste during the warmer spring and summer months in order to best enjoy the beaches and other seaside activities such as boating and windsurfing.
Winters (November to January): Temperatures in Trieste tend to stay around 8 degree Celsius during mid-winter, rarely if ever dropping below the freezing mark. As a result, fog, frost and snow are experienced. So this time of the year is off season in Trieste.
So, the best time to visit Trieste is between March to August.