Bucky, a tall, dark brown, barrel- chested horse with large shoulders, is a gentle giant whose best manners are reserved for a veterinarian.

When Dr. Virginia Reef approaches his stall, Bucky whinnies a welcome; when she opens his door he nudges her shoulder. ''Look at that,'' she said the other day. ''He's expecting his carrot.''

Like numerous other animals, he owes his life to the skills of Dr. Reef and her colleagues here at the New Bolton Center, a rural campus of the University of Pennsylvania's School of Veterinary Medicine.

Because of the center, its people and scientific laboratories, Mystic Park, a 5-year-old, can once again enjoy the pampered life of a multimillion-dollar stallion standing at stud. Temugin, a stallion, may soon rejoin him.

Both are standard-bred sires that earned hundreds of thousands of dollars as harness racers. Temugin holds two world speed records. Research and Teaching

New Bolton, established in 1952, operated as a university field station until 20 years ago. It is now one of the veterinary school's two campuses and is a hospital as well as a research and teaching institution specializing in horses and other large animals.

With a staff of 260 people, including 70 veterinarians, rotating classes of 35 to 40 fourth-year students, and thousands of patients, it has reached one of its goals, Dr. Robert Marshak, dean of the veterinary school, said the other day. ''A main goal,'' he said, was to grow and to avoid ''a field station mentality,'' that of a facility with limited resources.

Dr. Marshak said the center's equine clinic, the world's largest, drew patients from across the country and abroad as well as from this horse-country area. Researchers say they are closing in on one of the mysteries of horse racing: why some horses are ''bleeders,'' developing pulmonary hemorrhages. The researchers are seeking clues to prevention.

They are also seeking cures to bovine leukemia. It was at New Bolton, a few years ago, that Virgil, the world's first test-tube calf, was born.

Bucky, a show horse, was the first horse given a pacemaker. The operation, performed last December. involved applying an ultrasound device in a technique commonly used in human heart care.

Dr. Reef demonstrated this. As she flipped a switch, the pulsing recorded image of an equine heart filled a television-like screen. In the operation on Bucky, she said, she was able to monitor a catheter tipped with an electrode as it was passed from the neck and down into the precise point in the heart where it corrected severe arrhythmia. Bucky's condition had brought on lapses of as long as 10 seconds between heartbeats, causing him to faint and fall, often injuring himself. A Pool and Operating Tables

Other equipment at New Bolton includes a swimming pool for horses, operating tables that can be tilted at varying angles and radiological cameras that provide pictures more detailed than X-rays on humans.

The pool helped save Mystic Park's life, said Dr. Kenneth Seeber, a veterinarian, who is the general manager of the sprawling breeding and brood mare establishments operating in three states by Lana Lobell Farms. They include the one at Hanover, N.J., where Mystic Park is now used for breeding.

Mystic Park was admitted to the Large Animal Hospital at New Bolton suffering from a condition eventually diagnosed as Potomac fever, once simply regarded as severe diarrhea but identified in 1979 as a distinct disease in Montgomery County, Md. It was often fatal. One symptom is loss of the hard protective tissue of one or more hooves. This is known as laminitis, or founder.

Hoof loss makes it nearly impossible for a horse to stand; when a horse cannot stand, it usually cannot survive. ''For a horse,'' said Dr. Seeber, ''it's like trying to walk barefoot over hot coals.''

It is for such horses and others, including those recovering from severe fractures, that New Bolton uses its pool. Attendants hoist the horse in a sling suspended from a monorail and lower the horse into the water. The body and head are supported by a fitted raft. Then, when the horse moves, the water's resistance prevents violent movement and new injury.

New Bolton is one of several institutions studying Potomac fever, according to Dr. Robert H. Whitlock, the center's chief of large-animal medicine. Veterinarians have now developed both a theory on its cause and a course of treatment.

''We think it is caused by a virus spread by an insect that takes the blood from one animal and puts it in another,'' Dr. Whitlock said. The fever, he said, causes the blood to thicken and clot. Part of the treatment is to inject a thinning agent and life-supporting substances such as potassium into the bloodstream. But the pool, Dr. Seeber said, helped keep Mystic Park alive while he was being treated. The Once-Hopeless Fracture

It also helps horses like Temugin to survive limb fractures that would once have left the owner no choice but to destroy the horse. Temugin is still under treatment at New Bolton after shattering a cannon bone, the short bone between the ankle and the knee. Dr. Seeber said the outlook was promising.

The cannon bone bears unimaginable stress during racing, Dr. Dean Richardson, an orthopedic surgeon, said as he demonstrated models of how such bones can be repaired. On his palm, he balanced fragments of bone held together with bolts and stainless steel plates.

Only a few years ago, said Dr. Richardson, who aided the surgeons who worked on Temugin, recovery in such a case would have been remote. ''We don't have all the answers yet but we're improving all the time,'' he said.

''You feel wonderful'' when a patient is saved, he went on, ''but the ones you remember are the ones you lose. That's what keeps you going.''