Honey Blocks don't stop horses or other rideable entities from getting damaged. Also, it causes the player to take damage if in Survival.
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Can confirm in 20w51a.
Can confirm in 21w03a.

Relates to MC-152258.
Can confirm in 1.17.
Can confirm in 1.17.1.
Can confirm in 1.18.1.
Can confirm in 1.18.2. It's important to note that this issue is not exclusive to horses and can be seen with all rideable entities that can take fall damage.
Can confirm in 1.19.
Can confirm in 1.19.2.

In 1.20 Pre-1 and 1.19.4.

Can confirm in 25w6a.