Big game hunting season begins in Mid August with Archery Hunting and continues thru Jan with anterless depredation tags. Spring Turkey hunts start again in April and May. If I didn't ride during hunting season, I wouldn't get any trail riding done.
I own horses because I got tired of packing deer and elk off the mountain. As the Forest Service started restricting back country access to motor vehicles, I found I had to replace my motorcycles with horses back in 1983. My horses are used extensively for back country travel during my hunting activities. So I have no fear of riding them during hunting season and continue to ride them even if I'm not hunting during the fall.
As a hunter from a western state, I have a huge respect for other hunters and expect them to abide by the same safety rules that I live by. You don't point your gun at anything you are not going to shoot. You always make sure there is a proper back stop behind your target. I don't ever shot at a deer/elk standing on a ridgeline where the rifle bullet could travel far beyond.
Here in Utah, our hunting license or tags dictate what we can shoot at. For example Hunters are given tags for Any Bull Elk, Spike Only Bull elk or Anterless Elk. A hunter has to Look at and determine
1st, Is the animal an Elk or is it a Deer, Moose, antelope, horse, cow etc.
2nd is it a Anterless elk, a spike bull or a mature bull. We have to look close enough at the animal to determine does it have horns and how many points does it have.
I can't just shoot at something brown moving thru the bushes. And sound shots are never an option. Why would I ever take the risk of shooting at a noise in the bushes and hope it was the right Species, Gender and Age to match my tag.
In addition the west is very different from hunting in areas back east. We are not nearly as concerned about the bullet traveling beyond the target. Since our mountains have such extremes in terrain. We almost ALWAYS have a mountain behind our target. Rarely do I have to consider, is there a farm house beyond those trees behind the Elk? I'm sure there are different consideration when hunting on flat land. Most modern high power rifles still have about 38-48" of drop in about 500 yards. I you are aiming at the chest of a deer ( about 32-36" off the ground) that bullet trajectory should drop and put the bullet into the dirt in less than 500 yards on flat land. I understand this is why many eastern states require or encourge hunters to hunt from elevated stands, because it points the bullet into the earth sooner than a bullet being shot on the same level as the target.
I exercise typical pre-cautions. I wear some orange, I often place orange or pink ribbons on my horses, Especially in the area of the head/neck where a hunter would have to look to determine the sex of the animal. And on the chest area, where a hunter would aim to take a lung/heart shot. I try to choose areas to ride, where I might not be as likely to encounter hunters. Elk hunting is in Alpine mountains, so I might ride in more desert areas during that week of the year if I wasn't hunting. You can also choose the time of your ride. There are probably more hunters out on Saturday than on say Wednesday. Also more hunters early and late in the day than at mid day. Since hunting season, usually means colder weather riding at mid day, is often a more comfortable time of day to be out than at Sun up.
It's unfair to classify all hunters as being careless or not concerned about safety. We usually do have a hunting accident or two each year. Mostly self inflected or somebody accidently shooting their friend. But that is a MUCH safer margin than the number of people killed each year in traffic accidents or by drunk drivers. Or even the number of murders that take place in a major city. There will always be the dumb smuck who breaks the rules, whether it be about hunting safety, reckless driving, or drunk driving. Just use common sense and think about the risk you are exposing your self to. If your area has a LOT of hunters and it's a problem to ride, Then don't.
Packing horse feed into our hunting camp
Orange Packs on a horse that is similar in color to elk.
Hopefully any hunter looking at this mule would realize he is the wrong color to be ANY type of wild game and the horns are in the wrong place. But even at that we have some orange ribbons tied to his saddle
If the bullet missed this elk, it will impact the mountainside behind it. There is no worry of it traveling a distance and hitting livestock grazing in a distant pasture.