The horse dies, so no, you can't use it because it's, you know, dead. If it's one you break in the wild or buy from a stable (such as the white and black Arabians), then you can get another one the same way once free roam is unlocked for John. But if it's a unique horse that can only be acquired one time (like Buell), it's gone forever. Any stabled horses owned by Arthur will also be lost.