It sounds like you wanted the dogs to be unable to see the chickens so they'd leave the birds alone, but I'm afraid that their senses of hearing and smell would negate that benefit. Even the old blind dog I used to have would know there were chickens behind there and leave no stone un-turned to get to them. And if a little mousey can chew through wood to get to food and shelter, so can any other predator. It's a lovely idea, and gee, I hate to add more cold water to your plans, but I'm afraid you'd be setting yourself up for losses.
If it's the appearance of a wood fence you are after, there are options. You could build a solid predator proof enclosure, then surround it with the wood fence for asthetics and a first (although weak) first line of defense. We put white lattice in front of ours because we live in town and it's visible to anyone walking or driving by. We wanted it to look nice but we don't expect that lattice to do the job of a solidly built run. The lattice isn't for protection - it's just for looks. The chickens are behind a cattle panel hoop run anchored to 8 steel fenceposts, it is covered in chicken wire against overhead predators, and the sides are hardware cloth about 2-3 feet up, which runs down to the ground and extends outward as an apron around the entire perimeter to discourage diggers. It worked too! Our 10 year old English Setter tried desperately to dig under the edge of the run. A broken, bloody toenail later she decided those chickens weren't worth the effort.
