Fury of Dracula 3rd ed. - Defeated Hunter and Skipping Actions
Correct. When you are defeated you determine the closest hospital (the one that is the fewest roads away) and then the figure is removed from the board and placed at the hospital at the next dawn.

If the combat was at dusk, the hunter only skips the night action. If the hunter If the hunter is defeated at dawn they would end up losing both their next night and day action.