Answer from April Reeves: There are two kinds of ‘hard mouthed’ horses.
The first is rare. This is the horse who has physical damage from abuse and mishandling of bits over a period of time. This mouth will show scars and hard, dense tissue with no nerve endings left. There are very few horses like this, and in my lifetime I have only seen 2. To get a horse this damaged takes incredibly rough handling. Once the damage is extensive enough, the nerve endings will never come back, and the horse is likely never going to work in a bit again.
The second is where most horses are: