Symptoms of a puncture wound include lameness and increased hoof temperature. Additional general infection symptoms may also occur.
As a horse owner, I should be sure to notify the veterinarian and in the meantime weigh whether I need to remove the object immediately to prevent it from kicking further into the hoof or I can wait for the veterinarian. If I decide to remove it, I need to keep the area clean and wrap the hoof in a clean bandage.