From this answer to Is damage taken when falling off a mount?:
The minimum distance to take fall damage is stated as 10ft.
However, if you are on a fast mount, you could potentially fall off while moving rapidly. In this case, you will have a significant amount of forward motion before hitting the ground. It's not clear to me whether this distance should be included in deciding whether fall damage applies (RAW).
Does fall damage only include the vertical component of a fall, or is the total distance applied?
As an example:
On a 6ft horse, dashing, the player can be moving forward at 120ft/turn (20ft/second).
If they are to fall, they will take 0.61s to reach the ground (6ft drop), and so will travel 12.2ft forward as well as the 6ft down (hypotenuse ~13.5ft).
As the forward motion is significant, and exceeds the 10ft minimum for fall damage – should the player take damage from this fall?