The Colt New Army & Navy revolver, chambered in .38 long colt caliber, was adopted by the U.S. Army in 1892, and it remained in service until it was replaced by the Colt M1911. The round's dismal performance against the Moro tribesmen in the Philippines (as displayed in this movie), forced the Army to re-adopt the 1873 Colt Single Action Army in .45 Colt, as a emergency response.
The revolvers used by Gary Cooper and David Niven in the movie, have Stag grips (or, probably, a plastic imitation).
Winchester Model 1897
The Winchester Model 1897 pump-action shotgun is prominently displayed in the movie.
Krag-Jørgensen M1899
The Krag-Jørgensen Rifle was actually a Norwegian design. The United States version, chambered in .30-40 Krag, was adopted by the US Army. This rifle had a distinctive magazine, that was integral with the receiver, featuring an opening on the right-hand side with a hinged cover.