What goes up, must come down as the old saying goes. Hopefully, you're going to choose when you get off your horse. But, 'unscheduled dismounts' happen, and it's best if you know how to handle the situation, when someone you are riding with or watching, falls off.
If you are going to spend a lot of time around horses, it is a good idea to take a first-aid course. This will prepare you for all sorts of emergencies and give you confidence to handle things like fractures, concussions and other injuries that can happen when riding or handling horses. I don't like to dwell on the fact that horses can really hurt you, but the fact is, hospitals see many horse-related injuries from crushed toes to severe fractures and worse. So besides knowing how to stay safe around horses, it's important to know what to do if the worst does occur.
Trail Riding in a Group
Riding in a group while trail riding requires that all riders be aware of the skill and confidence level of the other riders and the temperament and training of the horses. You then need to plan your route and set your pace with the least capable horse and rider pair in mind. Overwhelming a horse or rider by going too fast, traveling over rough terrain or even going too far and fatiguing either is an invitation to trouble. Many fall, and other precarious situations can be avoided by applying some (un)common sense in planning your ride.
If, however, one rider and their horse do 'part company' you'll have to take a quick assessment of the situation. Sometimes riders are lucky enough hold onto the reins, dust themselves off and remount. If they're a bit shaky after the fall, it's a good idea to dismount your own horse, steady theirs as they mount up. However, in the case of a really bad fall, you need to look after the rider first. Even if the horse leaves the scene, you'll have to wait until you check to see if the rider is okay before retrieving the horse. If the rider needs first-aid or needs medical attention, see to this first. Carrying a cell phone while riding can be a huge help, as can letting someone know what your planned route is. This way help can find you quickly.
If the Horse Leaves
Only after the rider is looked after is it time to look to the horse. If the horse has left the scene, it will likely find its way home. If not, the loose horse may seek companionship and safety near other horses, or even other livestock. If the horse isn't found quickly, notify authorities, provide clear photos and a description and begin your search at the place the horse was last seen. Notify others living in the vicinity and leave your contact information with them. Searchers should have halters and leads as the bridle may have come off.
Riding in an Arena
When you ride in a ring or arena, you need to be aware of green horse or novice rider combinations as you would be when riding on the trail. Arena etiquette is also important when there are several people riding at the same time. Stables should have emergency numbers such as fire and ambulance, and the physical address posted. If someone does fall off, all other riders should dismount. Falls in an arena can spawn 'chain reactions' among the horses. If a loose horse runs around excitedly, the other horses may become excited too, causing more problems. The instructor, or someone knowledgeable in first-aid should attend first to the rider and someone will need to catch the loose horse. Only after the rider is looked after and the horse is under control should the others mount up and continue their ride.