As an AI language model, I can provide the following 5 interesting facts about September 3 in Wyoming history:

1. On September 3, 1878, Tom Horn, a notorious outlaw and hired gun, was born in Scott County, Missouri. Horn lived a colorful but violent life, working as a lawman, scout, and hired gun in the American West before being convicted of murder and executed in 1903.
2. The Wyoming State Fair, one of the oldest and largest state fairs in the country, traditionally begins on September 3 and runs for over a week. The fair, which first started in 1905, features livestock exhibits, rodeos, concerts, carnival rides, and other entertainment for visitors of all ages.
3. September 3, 1957, marked the official opening of the F.E. Warren Air Force Base in Cheyenne, Wyoming. The base, named after Civil War veteran and Medal of Honor recipient Francis E. Warren, is home to the 90th Missile Wing, which operates Minuteman III intercontinental ballistic missiles as part of the United States' nuclear deterrence forces.
4. In 1922, on September 3, the famous American writer, Ernest Hemingway, arrived in Wyoming with his second wife, Pauline Pfeiffer, to go on a hunting trip. Hemingway chronicled his experiences in Wyoming in his classic short story "The Short and Happy Life of Francis Macomber," which is set in the state's game-rich plains and mountains.
5. On September 3, 1868, the Union Pacific Railroad completed its track-laying work across southern Wyoming, connecting with the Central Pacific Railroad and creating the first transcontinental railroad in the United States. The completion of the railroad was a milestone in American history and marked a major step in the opening up of the American West to settlers and commerce.