poor guy!!! they may not have mistaken him for anything, lots of hunters get drunk or just aren't as carefull as they should be, stupid idiots. lots of shots miss the target. a 22 could easily travel about 300-500 yards (not accurately though), if it didnt hit any limbs or leaves. the holes look a little too large for a 22 though, how large are they? a 22 is smaller around than a pencil, and if it hits and expands (especially a hollow point) it will get about twice as big around as a pencil.
when I was 16 we went out to feed our horses one morning sometime around this time of year. because of the cold weather overnight and forcast for rain/sleet we kept the horses in their stalls overnight. one of our geldings was acting perfectly normal but when he turned around (getting excited about feeding time) we noticed a arrow sticking out of his left hip. it had come through the metal wall of the barn, about 20 feet up the wall there was a hole in the metal. we had wood panels from the ground up to about 6-8 feet incase one of the horses pawed or kicked at the wall their hoof wouldnt go through. so the arrow had to travel across 25-50 feet of pasture and then go through the wall while falling down toawrds the ground. it was sticking out of his hip almost straight up and down, and was stuck in about 3 inches deep in his muscles. the vet came right away (cool thing about large animal vets, house calls) and removed it and I'm pretty sure stitched it up and gave us some meds to put in his feed, may have been more to that but it was a long time ago.
anyway, hard to tell from the picture but the holes look too large for a 22. deffinetly wasnt a hollow point of any caliber because the holes look the same size. with a hollow point or any soft bullet (plain lead, not lead coated with brass) or hunting bullet (for deer most hunters use a semi jacketed bullet, most of the bullet is covered by a layer of brass but the tip is exposed soft lead so it expands making a bigger wound and causing more internal bleeding) the entrance wound is about the size of the bullet and the exit wound is about 2-4 times larger than the entrance wound.
he sure is one very lucky dog.