What was Big Willy Shakes going for?
As far as famous battle words go, this one is pretty cryptic. Sure, Richard's horse has died, but he wants way more than a simple stallion. He wants to be able to fight, and without a horse, he cannot. Richard desperately yells for a horse even though there is no hope of one.
You've probably guessed already that Richard is not to be trifled with. He wants his kingdom and he wont give it up. To anybody. Ever. For realsies. So when he offers it here for a horse, we know he must be desperate. Now he's not actually offering to give away his crown. He's actually saying how much he wants to keep it. He needs to fight Richmond and will give anything to be able to do it. It's a little case of hyperbole.
Shakespeare came up with a lot of cool stuff that we still say today, but this quote was a hit in his own day. It was so popular it was already being parodied. Think SNL but Elizabethan style. John Marston, a playwright around in Shakespeare's day, wrote "a boat, a boat, a boat, a full hundred marks for a boat!" and "a fool, a fool, a fool, my coxcomb for a fool!"