The trumpet is left behind when Jonah Williams leaves the cave. While he is returning and crossing the bridge/walking to the cave, he has the trumpet at his side. As he arrives at the cave, he again is without the trumpet. He retrieves it once he is back in the cave.
The shown lever-action arms carried by the soldiers were not issued to US units. 1873 saw the initial issuance of trapdoor Springfields, a breech-loading single shot rifle or carbine using a .45 caliber metallic cartridge - the same arms carried by Custer's troopers at Little Big Horn.