This works for all versions 1.16.10 or later. 

I found that the horses that were tamed before 1.16.10 are "super horses" (cannot take damage). offspring of said superhorses do not have this characteristic. Superhorses sometimes appear with up to 200 health.

This may be hard to recreate as the horses that are affected are from an earlier version.

recreation:

1: get a device on 1.16.0 or before

2: tame a horse

3: update world/device to 1.16.10

4: hit the horse with a fire aspect sword, then mount it to observer its health

Observed results:

horse tamed before 1.16.10 does not take damage by any means {lava, ravines, harming II)

Expected Results:

The burning horse takes damage.

Update:

Horses that are being ridden no longer take fall damage, no hurt sound or red flashing.

EDIT 2022

Bug is still present in versions 1.17, 1.18, 1.19.

Since I am on mobile it is difficult for me to upload a world. I have provided world.dat and a link to the world files. Do excuse the strange name.

LINK TO FILES:

world.zip