Go to the Train Station where you go to at the end of the game. During the last mission, you'll use the cart with a cannon to blow up the entrance to the mine.

After you beat the game it'll be closed again. There'll be a corner in between the cliff and the entrance on the left.
Take a horse and spur it into the corner and run into the wall.

After that you can spur your horse into the door to get out.

If that doesn't work spur into the wall and then press X right before you touch the wall to slide.