"MY" take....
First....I'm not being critical...just offering advice.
#1 - Finding the arrow in a timely fashion is PARAMOUNT to knowing your next move.
#2 - I think you would have seen the arrow sticking out of her if it had stuck in and been broken off.
#3 -
Could an arrow snap in half from impact on a rock or collision with something else?
YES! I told Rob I was glassing the other night....and saw something in a tree about head high. It was an arrow. I INSTANTLY knew the story of it. Last year....before I took the buck I just got back from the taxi....I had a shot at him (Thanksgiving Day) at 30yds. It was dusk....and I didn't see a small limb in front of me. I release my arrow and it sounded like an explosion. New lumenok.....gone. All I find is the fletching end. I didn't even look for a black shafted arrow with no markings in that brush. But....now I know where it is!
I'm going to take a photo of it in the tree.....as soon as I get that far into my woods on a day hunt. But to answer your question.....most definitely a limb can do that to an arrow.
I'd say you missed....but I can't express how much that arrow will tell you....and I'd do everything in my power to find the arrow before I did ANYTHING else (in the future).
Good luck