Coming in a bit late on this discussion, but I'm getting the impression you may have a bit more research to do before considering buying a cockatoo. They can be wonderful birds, but they really are one of the most difficult parrots to own. If you don't have 100% dedication or a whole lot of experience with large parrots, a cockatoo may be a bit much to handle. For starters, while it is nice to let a parrot hang out outdoors in warm weather, they aren't "aviary birds" who will be happy to live alone outdoors year-round, no matter how safe you make the cage from predators. You can have the fort-knox of parrot cages, but its not going to stop the parrot from being lonely. Parrots are flock-animals, and belong primarily indoors with you and your family. Cockatoos especially are attention-needy, and need a good 6+ hour time commitment from you each day to socialize and play with them. Think of them as feathery toddlers. Would you stick a 2 or 3 year old child out in the yard all day, every day and "bring it in at night"? If not, you shouldn't do that to a creature who is as intelligent as a 2-3 year old child. A large parrot belongs indoors, spending LOTS of time outside it's cage with the family every day.
Also, you can have no neighbors for 100 miles, but that doesn't mean YOU'RE going to be "unaffected" by the noise just because the bird is outside. Trust me, doors and windows make no difference when it comes to a cockatoo on full volume. My parents have one of the smaller cockatoos (goffin) and let me tell you, that itty bitty pigeon-sized bird makes a screech that sounds like nails on a chalkboard amplified to a 1000 decibels. You can hear him 2 blocks down the road from inside the house, further when he's out on the patio getting sunshine. In addition to being excessively loud, he is excessively destructive and highly intelligent. You could not imagine the amount of damage a creature that size can do, and he's not even neglected, he's well loved and out of his cage all the time. He once disassembled his cage from INSIDE, enough to escape and tear up the house (turned the stove on and pulled all the knobs off, flung mail everywhere, ripped all the couch pillows up, flung any decoration he could move, let the other parrots out of their cages to join in the fun, he is a little crap-head lol). My dad thought he got burglarized when he got home, but it was just the bird having a few hours of unsupervised destruction. And he is a small cockatoo, the bigger you get, the more "deviousness" you will get. The truth is, very few people are ok with the natural and normal behavior of cockatoos. My parents are in fact the ONLY people I have ever heard of who have had their cockatoo for more than 10/15 years (they've had him 39 years). Plenty of people have other species of parrots that long, but it's very very rare people have cockatoos for a long time because they have natural tendencies that do not mesh in the average home. Not saying it doesn't ever happen, but more cockatoos are destined for a lifetime of misery than a lifetime of happiness in domestic homes. Many cockatoos are destined to pluck themselves bald and chew holes in their chests because they are bored and do not get enough love. Most cockatoos will go through 7-10 homes in their lives. Most have a complete change from cuddly love-sponges as a juveniles to rather vicious to anyone but their perceived mate as they hit sexual maturity. PLEASE do A LOT more research before you get a cockatoo.
IF you just want a pretty white bird(s) for an outdoor aviary, why not get a couple doves? Obviously, you would still have to look into the predator concerns, but those kinds of birds are much easier care and a million times more suited to living in an outdoor enclosure with little to no human interaction than a parrot.
