We don't have anything so dangerous as bears around here, but it doesn't surprise me. If you get a horse that has a high protective drive for their territory and their herd, then they will most definitely be aggressive toward anything they deem a threat. Most my horses will just ignore whenever a dog gets in their pen or anything like that, but my Mustang Dobe is a whole other animal. I am convinced that if he had stayed in the wild, he would have ended up a herd stallion. He is very aggressive toward everything that challenges him even a little bit. He is the alpha of all my horses, even the drafts.
When it comes to working cattle, he will bite, kick, pin his ears, and snake his head much the way a stallion will that is protecting his mares. There have been a couple of times when I was riding around town and there was some loose dogs that charged. Dobe's first instinct was to spin toward them and take his aggressive stance. If they kept coming, he would charge and go after them. In that instance, I would just give him his head and let him teach that dog some manners.