Any wildlife encounter can be traumatic for both horse and rider, whether it's a bear on the trail, or a rabbit that suddenly bolts from cover, or a large turkey suddenly flushing from behind a bush. Any of these can be the beginning of an exciting ride. And none of them can be totally anticipated or prepared for. But the more you know about wildlife, and their habits, in your area, or where you are going to be riding, and the more you prepare your horse, the more you can avoid a potentially disastrous encounter that could ruin your day.
BEARS In our area, all bears are black bears, not Browns or Grizzlies. While bears come in all colors from white to solid black, the two designations refer not to color, but to two different animals. To us, the difference is significant, but not so for the horse. While Black bears are seldom aggressive, your horse will not know that. It does not matter to him what species it is, any encounter will be a reinforcement of his innate fears of the 'boogyman in the woods' that his momma and all his friends told him about.
* Keep a flashlight handy, and sleep in moccasins. You will probably need to check on the horses several times during the night, and if there is a wreck, it's much better to have those on your feet than to go dancing around in the dark, barefoot. I always have a pistol handy, but have never really needed it. More for my own peace of mind than anything else. As a Colorado Law Enforcement officer, I would strongly suggest that if you carry a gun, at the very least complete a Hunter Education or other Gun Safety course. Again, training , preparation, and education.
* I have used many different setups for keeping a horse over night, from tying him directly to a tree, using a one-legged hobble, turning them loose with a two legged hobbles, using a high line, and using a portable corral. The worst arrangement is tying them directly to a tree. I've used that more than any other method, but now it's a last resort. Many horses will not stand still all night, but will paw and complain and keep you awake. A high line works better, but it's not foolproof, and a horse can still get into problems, or spend the night pawing and complaining. I've had them roll and get tangled up in the rope. From my experience, the portable electric corral with a D-Cell battery operated power supply, is the way to go. Your horse will spend the night eating, and in the morning will be ready to go, not concentrating on filling his belly. He will stand quietly all night, and you will sleep soundly.
* One note of caution: get a book, and learn to identify noxious weeds. Nothing would be worse than putting a corral up in a field of loco.