Sixty degree weather is typically considered somewhat chilly, therefore it would be appropriate to wear longer sleeves and pants, or shorter skirts and tights. In general, dressing in layers, such as a light sweater over a T-shirt, is a good way to be prepared for anything. Layers can be removed if the temperature suddenly rises.
An individual's preference in style and sensitivity to hot and cold can play major roles in what is appropriate for a 60 degree day or night. For example, those who tend to feel the cold more easily may want to wear a warmer coat or add a scarf and a hat. An additional sweater or light jacket might also be comfortable. For those who tend to feel hot or don't mind the cold, 60-degree weather doesn't call for a lot of warm clothing.