It depends on where you are, and how deep your pond is. My pond is about 5' x 7', and 29" at it's deepest. If you have cold winters, your pond should be at least 2' deep, preferably 3'. I live in New England where the surface freezes over each winter. You will need a pump and filter to clean and aerate the pond year-round, and if it's cold in the winter, a floating de-icer. If the surface of the pond freezes over, the trapped gases beneath will kill your fish. My pump does bubble at the surface of the water, but it still froze over a few times last winter a few times, so that de-icer saved my fish. You will also need to regularly feed your fish in the warmer months, the occasional insect or plants aren't enough. Once the temps fall below around 50 degrees, they cannot properly digest food.
There are several kinds of goldfish that are hardy, such as Comets, Shubunkins, and Sarasas. They need about 40-50 gallons of water per fish. They grow to about 12" in length. Koi are harder to keep, they grow as large as 36", and need at least 1000 per koi. They are also very messy, and need a good filtration system.