There are a few cases of horses who have had lower leg amputations with prostheses used, but it is a tremendous amount of weight on a small area, making pressure sores more likely than in other species, and it is also quite a commitment of time and money to make the custom prosthesis, fit/modify it for the horse, and then change the padding and maintain the health of the stump. IOW, it’s possible in some situations, but not feasible for most owners. They also have to not founder while the stump is healing and they’re standing on 3 legs.
Repair of fractures depend in large part on what was fractured and how badly, the size and temperament of the horse - bigger horses put more strain on implants and casts and are more likely to founder than ponies - and the time and financial commitment of the owner. Costs can be in the hundreds of dollars for several sets of radiographs and cast changes to $10K++ for complex cases requiring multiple surgeries, long hospitalization, time in a sling, etc., and people are more hesitant to spend money if the prognosis is uncertain or if the horse is not going to be a riding horse anymore. As mentioned above, regardless of the type of fracture, the horse has to strike a balance between resting the leg enough to allow the fracture to heal and not developing laminitis in the other legs, which is not always easy or possible.
There are a number of fractures that are routinely repaired. Racehorses are prone to condylar fractures, in which there is a diagonal split in one side of the cannon bone; these are relatively easily repaired with a few screws. They are also prone to so-called slab fractures, in which a carpal (“knee”, really like our wrist) bone splits in two. Slab fractures may resolve with just stall rest and time, or they may be surgically repaired - arthritis may develop in the joint, preventing future racing, but the horse’s life is rarely in immediate danger. If a horse fractures its coffin bone (the distal phalanx, inside the hoof), a special shoe can be applied which helps make the hoof more rigid; the hoof acts as a natural cast, and the prognosis is excellent unless the fracture affects the joint.
At the other end of spectrum from these routine fractures, grossly displaced fractures of the large bones of the upper leg, such as the femur, are much harder to treat, and implant failure is common in those that are treated. Most people choose to euthanize horses with displaced fractures of the long bones above the carpus and tarsus, although hairline fractures can sometimes be managed by stall rest, preventing the horse from lying down, and a good dose of prayer that it doesn’t come apart catastrophically.
In general, if a fracture disrupts the cartilage bed in a joint, the prognosis for full function is poorer and arthritis more likely. In some cases, the joint can actually be surgically fused - the cartilage removed and plates implanted across either side of the joint to encourage the two bones to fuse together - as part of repairing a fracture, but this doesn’t always work, and if you manage to fuse a high motion joint, the horse will always move with a significant gimp (and hence be a pasture ornament, not a riding horse).