
LogantheBard |
Feat from the core rulebook:
While mounted, you can ride down opponents and trample them under your mount.
Prerequisites: Ride 1 rank, Mounted Combat.
Benefit: When you attempt to overrun an opponent while mounted, your target may not choose to avoid you. Your mount may make one hoof attack against any target you knock down, gaining the standard +4 bonus on attack rolls against prone targets.

Some call me Tim |

I think your first thought of sized-based damage secondary attack is reasonable. The universal monster rules cover what natural attacks typically do. Large creatures typically get 1d6 damage.
I could see some argument that a bear should be able to use is natural claw attack. The difference is only a few damage points. But since it is damage from trample, essentially stepping on the intended target, versus taking a good swipe as if it was fighting normally the reduced to-hit and damage make sense. Plus it avoids someone finding some rideable beast with a massive claw attack and exploiting this trick.