Being honest, I don't know but I don't think so. At least, I'v never heard any horse was caught on branch in my area. Actually, if you think about it, it's same as if you have halter on (and almost every single horse in my area have halter on). Look at this muzzle: http://www.horse.com/products/sku-BRK61.html
It looks like a halter. That's the one borders at the farm where I keep mine use.
I know that ponies develop all these hoof problems because of grass (big horses too, but less). So it's certainly safety issue. May be if you don't like the muzzle idea you may think about moving your horse to different farm with hay diet.