Actually, a dog will have far less impact on the environment than a human, assuming the following extremely important items: (1) the dog is trained not to bark, (2) the dog is trained not to chase wild animals or is kept on leash, (3) his waste is buried--use the same treatment as for human waste. Certainly four soft paws on an 80-lb. dog are far easier on vegetation and soil than two trail runners with waffle soles on a 180-lb. human! It's important that the dog be current on his shots and receive anti-flea and tick medication, to avoid disease (either spreading it to wildlife or, more likely, catching it from them).
Then there is the dog's effect on the other humans on the trail. Many normally sweet-tempered dogs get upset in a strange place and start acting aggressively, especially when they run ahead of their owner (which should never be allowed to happen). Many of your fellow-hikers are nervous around dogs, usually as the result of bad childhood experience. Horses, of course, being creatures that survived for millenia by running first and asking questions later, can go into a tizzy around an excited dog, with possibly fatal results.
It's the dog owner's responsibility to keep the dog leashed or walking behind, to control the dog at all times, to scoop and bury the p**p.
My dog is a source of great joy to me on the trail and helps keep me warm in the tent at night. He loves being out there too--every time I get his pack out he starts jumping up and down! I also see more wildlife when I am with him, because he becomes alert long before I know anything is there. I do try to make absolutely sure he will not bother either man or beast when we are out there!