There have been a lot of sensible responses on here about self-defense on the trail, There have also been some big misconceptions.
First off, not everyone who hunts is a drunk. Also, I would like to see the law that states someone cannot carry a firearm before hunting season starts. Believe it or not, there are more hunting seasons than just deer season, and believe it or not, some hunters put a great deal of time and effort into the pre-hunt. This also leads to the point that the 2nd Amendment is not about hunting, it is about the right to keep and bear arms. It says nothing about hunting in the Constitution.
When I go out on trail rides, someone approaching me is the least of my concerns. It is very seldom I see a person where I ride. I do come across people on mountain bikes on occasion, and have never felt threatened by one of them. Still I carry both a large caliber rifle and a large caliber handgun on each and every ride I go on, and sometimes my pepper spray as well. Although I do not feel fear when I see a fellow outdoors person in the mountains, I do have a great deal of respect for bears, both black bears and grizzly bears, especially if they are with cubs. I do not fear the wolves nor do I fear the mountain lions. They are more afraid of people than I am of them, and they will keep their distance. The problem with the bears is that you can surprise a sow with cubs and then all heck is going to break loose. So it is important to allow them to hear you, simple talking, to a friend riding with you or your horse. Whistle a tune while you ride. Put a bell on your horse. These will all work fine to allow them to hear you.
I realize some folks do not approve of guns, do not like guns, are afraid of guns or do not understand how guns work. That is fine, and a great alternative and very effective means of protection has been mentioned, pepper spray. If this is your choice, please get the larger canister which will shoot out a spray to 30 feet. Do not get one of the chemical make believe sprays as they will deteriorate over time. Get one that is made with real peppers. Have someone who knows about bear spray/pepper spray tell you if it will be no good over time. Most have an expiration date on them, that does not necessarily mean that it will no longer be any good, it sometimes means that the manufacturer want you to renew your purchase.
Most situations can be controled or avoided with plain common sense. Now go out and enjoy a nice lone ride with your four legged friend.
The best thing for the inside of a man is the outside of a horse