I know it defies suspension of disbelief, but what official rule can I show a rules lawyer player that "proves" a horse can't start a grapple?
If the answer needs to distinguish between animal companions, paladin's warhorses, polymorphed player characters, etc then please cover all the cases.
Also, mentioning if there is any rule giving a penalty to grappling for having the form of a horse would be nice, even if it doesn't precisely fit the question title.
Best Answer
Yes, a horse may grapple.
Monster Manual p273:
Horses have a grappling score, there aren't any special requirements excluding them from being able to grapple, and there's nothing saying horses can only react to grappling. The grapple rules, even employed literally, require a grappler to grab and then be capable of holding their opponent - the horse can do this (beginning with its mouth), so it passes.
All in all, a horse may grapple, because there is nothing mechanically preventing them from doing so.
Furthermore, the first paragraph of the Grapple entry in the 3.5e PHB:
Holding you down purely with body weight is a perfectly legitimate grappling tactic. As @BESW mentioned, a horse can stand on you, and from there, instead of clawing you, it can stomp on you.