You will take damage except as below. The reasoning is that you have no time to prepare.
Soft Fall becomes "Avoid being crushed by the massive amount of horse flesh that is rolling around by you". This is to avoid even more damage from the crushing of a VERY heavy animal. Should the character make a high enough roll (i.e. beat the DC by, oh I don't know, 10 or more) then I'd allow them to make the Soft Fall as per normal rules. They just did so well and seeing knights do cartwheels in full plate is just damn funny in my head.