A saddled horse that's not being driven does take fall damage.

An un-saddled horse being ridden by a player does take fall damage.

Un-saddled and riderless horses do take fall damage...

But while saddled and driven by a player, they do not take any fall damage.

To reproduce:

1. Tame a horse.
2. Equip a saddle onto the horse.
3. Ride it off from a high place.

With a fencepost high-up and attaching a lead to the horse and said fencepost, you can easily test the scenarios above yourself, as mounting the horse will break the lead, causing it to fall... or detach the lead yourself.