Additional information from MCPE-151214:

The health display of a mob you're riding occasionally hides the mob's max health. However, it corrects itself upon the mount's health being updated (being healed or taking damage). This is most noticeable on striders and pigs since they do not heal naturally, but it can be caught on horses.

To replicate:

1. Get a mob, preferably a strider or pig.
2. Mount it and take note of its HP
3. Now deal any amount of damage it, just don't kill it.
4. Move far enough away from the mob so that it unloads.
5. Go back to the mob and mount it.

Expected Result:
You see your mob's health, that it has taken damage and is not at full health.

Actual Result:
You won't see the empty, or half-hearts of your mount, so it'll look like your mount is at full health.

A horse will show its max hp as its health when you saved and quit the world:

Steps to reproduce:

1. Get a horse
2. Damage a horse
3. Save a quit
4. Reload
5. Notice the change in apparent max hp