In the scenes where Anna and Sarah first escaped they were riding bareback then there were times you could see saddles on the horses, especially at the river where they're recaptured - you can see them bareback, but when Anna's horse goes down you can see a saddle on her horse.
As the Indians ride away from the camera, the horses they are riding are shod. Indian horses would not have horseshoes.
The movie is set in 1868 but the lyric of the song sung during Anna and Daniel's wedding, 'O Perfect Love', was written in 1883 and set to music in 1890.