Broken bones occur fairly commonly in dogs and cats. Treatment options will vary, depending on the location and severity of the break. The major determinant in whether a broken bone can be treated more conservatively with a splint or if surgery will be required is the location of the break.
A splint or a cast must be able to immobilize the joint above and below the fracture. If both joints are not kept completely still, every time the joint moves even a small amount the pull of the muscles will cause the broken ends of the bone to move. This causes pain and disrupts any healing that has occurred. Even 1 millimeter of motion between the broken ends of a bone can undo any healing that has taken place. At best, this will prolong the amount of time the patient has to wear the splint because it prolongs the healing process. At worst, this chronic trauma can cause the healing process to stop which causes what is called a nonunion. A nonunion is essentially where a broken bone does not heal and is unstable. The only option if a nonunion occurs is surgical repair of the fracture.
In some cases, your veterinarian may recommend surgery for a fracture that seems like it should be able to be treated with a splint. One common example of this situation is when a toy breed such as a Chihuahua or Miniature Pinscher breaks their radius and ulna (the two bones of the front leg below the elbow) down near their wrist as in the radiograph above. Surgery is often the best choice for this situation because the lower part of the front leg does not have a robust blood supply. These fractures have a high chance of becoming nonunions so surgical repair is often recommended at the outset to give the best chance for a full recovery.