Yes, if you acquire the white Arabian horse as Arthur in Red Dead Redemption 2 story mode, you will keep it when you play as John [1]. The horse will transfer over to John if it is stabled or hitched at the time of Arthur's death. This allows you to continue using the white Arabian horse in the later stages of the game.

Learn more:

1. If you acquire the white Arabian horse as Author in Red Dead ...
2. Will the white arabian horse respawn? :: Red Dead Redemption 2 General Discussions
3. Red Dead Redemption 2 best horse guide: the white Arabian - Polygon