I would think that unicorns would charge in with their horns only out of desperation, as you would almost have to stare at the ground to do it. I would think even if you did make solid contact with you opponent, you could really mess your neck or back up from such a high impact. Two ponies charging at each other would almost certain kill both of them from the sheer force of it, let alone a horn through the eye or mouth. Hmm. All contact sports have a semblance of violence in them and I really do concede that tilting has martial origin. However, the entire process of the joust has a lot of ceremony and can be relatively safe if both tilters (almost said riders) know what they're doing. I would think Equestrian jousting would be even safer by cutting out the uncertainty of the mount, both knights are in complete control of what's happening. I would think the primary weapon for the REA would be the lance, it would almost seem odd to not have every soldier equipped at least with a light lance to at counter charge other advancing or flanking formations if you can. This would lead to opponents to use something akin to a phalanx to prevent the almost certainty of an Equestrian charge, which I would think would be countered by cataphracts with heavy javalins or heavy maces to break their spears. [/over analyzing pony warfare.]