I'm not too big a fan of it myself. I mean, the point of germ warfare is to kill Alot of people... closed up in a city with the black plague was effective for killing off a garrison, but at the same time it shoots all strategy in the foot. You've basically gotta' do it, and run; otherwise your now infected.
Disease soaked towels killed many many people... but again: not a whole lot of strategy here, we're just killing a whole crap load of people and backing off while it happens.
Most of the times it's done in games though, it's a just a minor annoyance. See: Stronghold 2. I mean, you get a diseased cow? Walk the heck around it's bloated corpse, and your fine.
Balancing what it would really do, with what isn't overkill or balance shattering is the real issue. Maybe... infection can happen, it can run throughout the castle to effect the units abilities to fight? Like, when you've got a cold and feel like death, not wanting to get out of bed? Do that in 40 lbs of armor now. But, make it so both sides can get it, either by handling the dead thingy launched over the wall, or by a diseased dude running out and taking a wee in the invading armies grain shed... so you really have to decide: "this is something that will make this much easier... or it could backfire and screw me over."
Also, cows hitting walls: Mythbusters did this with unfrozen store chickens... same result I'd imagine.