Arbequina olive trees are native to northeastern Spain, which has a warm, temperate climate. These trees do best outdoors in USDA hardiness zones 8-10, and indoors in zones 4-7. They are among the more cold-tolerant varieties of olive trees, able to withstand below freezing temperatures for short periods of time. If you live in zones 4-7, you can keep your olive tree outdoors for the majority of the year, but should bring it indoors during the late fall when the temperature drops below 50 degrees Fahrenheit.