Horses often escape because they are bored or because they see food just out of reach. Once out, they may hang around and eat the food, or they may start wandering. Multiple horses together are more likely to travel far. Horses don't like to be alone, so they will usually stay close to the group.
It is critical when assisting with a missing horse to engage people who know horses and how to handle them. Chasing or attempting to herd horses will frighten them and could cause a traffic accident or other potentially fatal injury. Carry a proper halter and lead rope and a bucket of grain, as many horses will respond to the sound and follow the person holding the bucket.
Rabbits can be tricky to catch, as the world is their salad bar. If they are well socialized, they may approach the owner or others offering favorite treats. More often, they will hop just out of reach. Some have been successful in capturing a loose bunny by luring it into a large cage or corner of the yard with an x-pen.
It is critical when assisting with a missing rabbit to engage someone who knows how to handle them. Like horses, rabbits are easily frightened and can injure themselves attempting to get away. Please read this page on safe and humane rabbit handling from the House Rabbit Society.
Reptiles cannot regulate their body temperature like mammals, so their life revolves around thermoregulation. This means two things: one, they may seek heat and be found in a sunny window or behind the refrigerator, or two, they may unfortunately end up in a cold location like a closet or under the bed where they will become so sluggish they can't move.
Understanding the behavior of the specific reptile will help you focus your search; for example, iguanas tend to climb, so are often found in trees or on top of cabinets. Snakes like to curl up inside things so may be found behind a couch or in the closet. Consult the herptile clubs in your area for more detailed advice.
Turtles and tortoises are notorious escape artists. Large tortoises are extremely strong, capable of pushing gates open and traveling surprisingly quickly. Conduct a search as you would for a dog, talking to neighbors and hanging posters. Also check animal shelters, as some do accept these kinds of animals, and check with your local herptile club or rescue, as found animals may be brought to them.
Smaller ones like box turtles are often found in the garden, either eating greens or looking for a place to hide and hibernate, depending on the time of year.
Large birds can survive amazingly well on their own. There are some well-known flocks of mixed parrots living around the U.S., the result of escaped pets banding together for safety and companionship. Obviously a bird with clipped wings will not be able to travel as far as one with full wing feathers.
If the bird got out of a window, leave that window open if safe. Some have had success by leaving the open cage outside the window, which the bird later returns to as a matter of routine. Search and report your bird missing over a large area, as many are found weeks or months later quite some distance away.
It is not possible for us to comment on every possible kind of pet that may go missing. We encourage you to contact one of our Missing Pet Consultants for assistance in your area. If they cannot help you, they can likely refer you to someone who can, or to experts on that kind of animal.