Consider what it would look like from the point of view of a bacterium in your eye. Your nose becomes the spaceship that is very close to the horizon. You see it flatten against it, as you're approaching it.
In fact, even people far away from the horizon see their noses flattened and red-shifted, only the effect is so minute that it's undetectable. The solutions to Einstein equations are continuous, so the effects of gravity fall off with distance but never disappear completely.