I had taken a lot of fire damage in peaceful mode. I noticed that while I was riding a horse, I regenerated my health a lot slower than when I was off the horse. When my hunger was below 9, I regenerated normally off of the horse, but when I was on the horse, I stopped regenerating, like you would in other difficulties. In order to recreate the event, take a lot of damage in peaceful mode. When you get on a horse, if your hunger is at 9 or above, you will regenerate slower, like in other difficulties. If your hunger is below 9, you won't regenerate at all, again, like in other difficulties.