You can't use the real-world fact that a horse is heavy to justify the insane cavalry mechanics in the game currently, because:
1. The weight of an object moving laterally doesn't (much) affect how hard you get hit. Gravity is a vertical force which doesn't really affect momentum. A 40 ton tank which hits you at 20mph is going to impart just as much force as a person who hits you at that speed. If you're standing in a faultline and a moving tectonic plate taps you at 2mph, you won't suddenly get knocked back because of the mass of the object (which is trillions of times more than a horse). Due to the latent elasticity in all objects there is also a limit to how much energy can be transferred in a hit.
Clearly, physics was not your best subject in school. Gravity itself doesn't affect horizontal momentum, but MASS does. The force of an impact is dependent on the mass of an object multiplied by its speed. The object being hit can usually react to some degree, and bend or move to absorb some of the velocity, so a tectonic plate moving at inches per year won't hurt you in spite of the incredible mass, (although it can break a concrete wall that has no ability to bend or otherwise absorb the movement), but faster impacts are less able to be absorbed in that manner. Being hit by a light object such as a thrown baseball moving at 70 miles per hour can be painful, but nowhere near as deadly as being hit by a 2 ton motor vehicle moving 70 miles per hour, because of the vehicle's far greater mass. A relatively light bullet is deadly at nearly or over 1000 miles per hour, since your body has practically no ability to respond to an impact at that velocity. A charging horse will probably not kill you on impact at 20-30 miles per hour, but it will very likely inflict some serious injury. At a walk, that same horse would probably do no more than to push you aside, however, because of your body's ability to move to absorb the relatively low-speed impact, as well as the lower (mass x velocity) energy imparted to the target.
As said, one of the major differences between a "war horse" and a riding horse was that the war horse was deliberately and extensively trained NOT to stop before impacting a person. They still could balk at charging a group of people, particularly with a several man deep line of shields. The horse won't charge at anything it THINKS it can't push aside, which is a big difference from charging a single person or a thin skirmish line.
The game could use some kind of "horse morale" factor to determine whether your horse will or will not charge to impact, or whether it will balk, veer off, or slow to a walk. Different kinds of horses would have higher or lower morale, so your riding horse won't intentionally run down an opposing soldier (it may accidentally run them over while fleeing), but your fully-barded charger won't so much as flinch at the idea.