Deer, coyotes, etc see in shades of grey.
This is not true at all and is a common misconception. Most animals in the deer family are referred to as being color blind. That in no way means they see in shades of gray. They very much see in color. They just don't see the same colors as most humans.
Many humans are color blind too, I know several including my son in law. No 2 humans that are color blind are exactly alike. They certainly see colors, but to them they cannot tell the difference between some. Some people may see green and blue exactly the same, and tell all other colors apart. Others may see black and red as the same while everything else looks normal to them. This is the same way deer see.
All the studies show that the blaze orange that stands out to most humans is a neutral color to deer. My son-in-law, can't pick out another hunter in the woods wearing orange. It looks like a dull shade of blackish red to him, it doesn't jump out as being un-natural. Other colors do. Probably similar to what a deer sees.
I've read that to a deer the color blue does seem much different than other colors. First I've heard of gray.
Most birds have eyes very similar to humans and it is generally thought they see pretty much the same colors as humans.
Camo clothes never hurts, and may very well help with big game animals. Exactly which shades of color probably doesn't matter all that much. Remember, the deer won't see the same colors you see. The desert camo will be just fine in your area. The green camo would probably work very well for deer too, even though it may be more easily seen by humans. As long as anyone is perfectly still camo is probably not needed. But no one is ever going to take an animal by sitting in the woods like a statue. At some point you are going to move, if nothing else to raise your gun or bow. Camo clothing can help hide that movement.