The reason this isn't a simple answer is because the term "cold-pressed" isn't a regulated term, but rather a marketing term dreamed up to help sell olive oil.  One can find definitions of "cold-pressed" out there, but those definitions are not regulated by any government or industry body, so it doesn't have any real meaning.

The term that is regulated is "extra virgin".  This is a term that was created in the 1960s to help consumers be sure of the quality of the product they are purchasing.  Virginity comes in several levels (with extra-virgin being the highest quality) and is defined by the International Olive Council (www.intrnationaloliveoil.org).  The USDA and the European Commission have slightly differing standards for extra-virgin olive oil, but they both conform to the IOC standards.

Here at The Olive Basket, our Extra Virgin Olive Oils are true extra virgin oils.  Technically, EVOO can only contain olive oil and nothing else, so our Infused Olive Oils and Fused Olive Oils do not fit the bill.  

Our Infused Olive Oils start life as true EVOO, but once essential oils are mixed in to create the desired flavor profile, they can no longer be called extra virgin.  While our Fused Olive Oils are produced using the same methods as traditional EVOO, they contain more than just olive oil, so they can't be labelled as EVOO either.  We are comfortable calling these products "cold-pressed" since they are made using the highest quality methods.