The Sam Elliott character tells the immigrants they are fools for having oxen for their train rather than horses. The truth is that most pioneers used oxen rather than horses for pulling their wagons west, unlike the depiction in most westerns. Oxen are slower but better suited for such a trip because they are stronger, able to endure under duress, are less picky eaters, are more sure-footed, can better pull fully loaded wagons up mountains, are less easily spooked, and, upon arrival at a destination, would be better suited to farm life.
They mention the "White Elephant" bar when they're in Ft. Worth, which still exists today.
Many of the scenes set in Fort Worth, Texas, were actually filmed in the present-day Fort Worth Stockyards historic district.
The significance of the year 1883: On March 1 of the year 1872, President Ulysses S. Grant signed the Yellowstone National Park Protection Act, and was passed by Congress in the winter of the same year, which officially cemented Yellowstone as the world's first national park. Eleven years later, in 1883, construction of the Northern Pacific Railroad (funded by primary investor and Philadelphia Financier Jay Cooke) reached the north boundary of Yellowstone National Park.
The name Yellowstone itself, refers to the sulfurous deposits, which tend to be yellow, that are found in and around the park due to geyser activity.