No. The color of olive oil has nothing to do with flavor or quality. Olive oil color varies according to the type of olive used and its ripeness at the time of extraction. A bottle labeled cold-pressed or first cold-pressed points to the method used to extract extra-virgin oil. According to standards set out by the International Olive Council, all certified extra-virgin olive oils are required to be first cold-pressed, so a label with this information isn’t particularly meaningful.