Historically, dealing with skirmishers was a pain if you weren't equiped for it. A force made up entirely of heavy infantry would typically end up being exterminated by skirmishers. That said, I've never had any trouble using cavalry to mop up the enemy's light troops in EB. If you're playing on hard/very hard battle difficulty, you must realise that the results are expected to be unrealistic, since you've asked the AI to cheat and make its troops uber.