I live in the woods on a mountain in N. GA, among mostly oak, maple, beech, sassafras and sourwood trees. The leafy carpet of various shades of brown, red, orange and gold seem to hide the darker red birds, like my RIRs I used to have, or my crazy mixed up girl who is 1/2 BLRW and 1/2 Blue Ameraucana but came out deep oxblood red with black ticking. You can barely see those colors in my woods. The Barred Rocks are well hidden and surprisingly, so are the blues since they really look like gray shadows. I lost my Speckled Sussex one day when she got spooked by the motor of the tiller. Took us awhile to locate her under a bush with her dark and spotted plumage.
The combs make a difference, too, though--doesn't matter if the bird's plumage blends well if a big red comb is sticking up. Pea or rose combs are harder to spot on the hens than singles are.
I also have a few white birds, the Delawares, and a Lt Brahma, though, of course, they aren't completely white, however, we have never lost a bird of any color to a predator in the over six years we've had chickens free ranging on an almost daily basis; at least, we haven't yet. Our time is coming, I'm sure. I credit alert roosters and good tree cover to inhibit hawk dives, plus our daily presence going in and out of the house and coops since we don't work away from the house. They never free range when we leave the property.