Would a horse be sufficient buffer to prevent injury when falling from a great height?

I'm writing a sci-fi story with some fantasy elements, and I'm trying to keep even the most outrageous moments grounded in the laws of our universe. This is one of those moments.

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The Situation

A man on horseback (Tarn) is at the top of a small cliff. There's a medieval-style battle raging on all around him, including in the field below. In that field, the commander of the opposing force has just decapitated Tarn's commander.

This is his chance. If he avenges his commander, Tarn will be sure to advance in the ranks. But he needs to get down there right now. He's not afraid of death.

With no easy way down, Tarn spurs his horse into a gallop towards the edge of the cliff. Before it can consider stopping, he drives his sword into its head and holds on tight as momentum carries them over the edge.

They hit the ground. The horse splashes, but Tarn bounces and lands on his feet with a stumble. He pulls his sword out of what's left of his horse's head and charges forward on foot.

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The Question

Could a horse plausibly break your fall in any significant way? If so, what's the greatest height this could be done from?

The horse and rider would be landing on grass and potentially soldiers in the middle of combat. If there are factors that would make this more likely to succeed I'd be interested in hearing them!

Bonus: if there are other elements of this that are implausible I'd be interested in hearing alternatives, especially regarding the whole "killing the horse you're riding with a sword" bit... but that's not necessary!

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My Research

Googling hasn't turned up much on this specific scenario. I don't really have a science background, but maybe this will help:

Average Horse Stats

• Weight: 500kg
• Length: 2.44m
• Width: 0.76m (don't judge my sources too hard)
• Height: 1.58m (from where the neck meets the back)

Based on a comment from Halfthawed, let's sayyy the height from stomach to spine is 0.67m. Source: I eyeballed photos of horses.

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Edit: Thank you all so much!

Okay, we've been beating this dead horse long enough. It became pretty clear right off the bat that the answer is a resounding NO: horses don't make good airbags.

That said, the answers that this question has received are SO comprehensive and helpful. We have:

• One based on practical real-world experience
• Two drawing from historical sources where people survived falls on horseback, one about a noble named Horymir, and one about a Mamluk
• One from more of a physics angle
• Several with very good tweaks to make this more plausible, like this suggestion to have the horse slide down a steep slope, and a few suggesting he aim for trees.

I am honestly blown away by this community. Y'all are amazing, and if I could collectively accept all of your answers I would, as they've all had some affect on how this scene will end up playing out. Speaking of, here's a roughly revised sequence of events...

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This is his chance. If he avenges his commander, Tarn will be sure to advance in the ranks. But he needs to get down there right now.

In the direction of his target, Tarn spots a cluster of trees whose branches reach up nearly as high as the cliff is tall. Perfect.

He spurs his horse into a gallop towards the edge of the cliff. It's a well trained horse, normally extremely trusting, but something has been off about Tarn lately and perhaps the creature senses it. Metres from the edge, the horse slams its hooves into the ground and sends Tarn flying.

The horse slides half over the edge of the cliff, barely holding on with its front legs as its rear ones kick fruitlessly at loose rocks and soil.

Tarn just nearly misses the trees, but through some combination of luck and skill, he hooks his battle axe onto a branch and is jerked into the path of several more. They break and bend under his weight as Tarn stumbles downward in a barely controlled manner before slamming into the ground below.

He crawls up onto his hands and knees, and his trusty battleaxe punches into the ground head-first, directly in front of him. Barely phased, he uses it as leverage to help him stand up.

Behind him, the sounds of clanking swords cease. Tarn turns, exhausted, and locks eyes with an enemy soldier who stands over the corpse of one of his own.

The soldier runs at him, sword raised. Tarn tugs on his axe, but it's stuck in the ground good. Tarn starts yanking at it with both hands, the screaming enemy only a few second away.

The axe comes out and Tarn raises it up high over his head in both hands-

His horse slams into the ground, flattening the soldier in an instant and erupting into a geyser of blood. Tarn is bathed in it.

He turns to face the commander. That seems to have gotten her attention.