The bug
icons.png appears to have two more textures dedicated to the horse's health bar, which are lighter versions of the horse heart, probably intended for displaying when the horse takes damage analogously to players. However, they never seem to display in game, and the health bar just abruptly decrements instead.
How to reproduce
Get on a horse or other rideable animal which has its own visible health bar
Cause the horse or other mount to get damaged
Note that the bar just goes down with no effects
Now take damage yourself
Note how there is a flashing effect in the actual heart portion to indicate damage taken
Other thoughts
The screenshots attached to this ticket were taken using the poison effect to inflict damage on the horse. Unlike with player hearts, poison seems to have no visual effect on the health bar at all, and the wither effect as well as being frozen similarly have no effect. I'd definitely recommend adding these for consistency's sake since not having them isn't optimal.
I'd also strongly recommend splitting icons.png into its constituent sprites (or at least some of them), as having them in an atlas like this is problematic for many reasons.
Can confirm.