Well... This just got complicated...... But, I just happen to have a sped up hydro.
So, like the others said, there's not much you can do. If you don't want to do @fatboy_dan
's last option, (it'll probably work, but it's a long hard project) then bigger and better tires are a must. You can also put something like a 6in pulley on the front, and that'll crank a little more speed out of it. The others say it's the worst thing you could do to it, but I've been running mine since December with a 6in on it, and it hasn't given me any trouble since besides some belt slippage. I may end up eating my own words but I don't care.
Now, if you plan on mudding it, then you have more problems. For one you have the cooling fan. That's on top or bottom of your imput shaft. If you get that covered in water or mud, or if you get a stick wedged in it, it's done for. You can replace it, but since mine isn't made anymore, it would've cost me $70, so forced a craftsman one for $15 to fit, and you'll have to drop the tranny every time it breaks. You may be able to protect it with some type of screen or something, but you'll never be able to protect it from water. Two, your drive system pulleys. Whenever my belt gets wet, I can barely get up the hill, so you'll need some crazy tension on your belt. And with that much tension, any plastic pulley will melt in no time flat. ALL the pulleys need to be metal. And three. If you swap the engine pulley like I did, in the winter you need to warm it up for a few minutes. That means DON'T USE FULL SPEED for the first few minutes. If you let it sit for a few hours, you'll need to do it again. You don't need to worry about it much in the summer because it'll already be warm on the inside. So, basically, it'll be fine splashing through puddles and stuff, but it won't come close to surviving FearlessFront style mudding.
As for working purposes, it won't pull anywhere near it's original towing capacity with the new engine pulley.
Now for normal mudding purposes, the best way to go is to lock the diff, much bigger tires with with mud tread, and a bigger front pulley. But, It's not gonna serve you well if you don't take care of it.
If your looking for plain speed and nothing else, the hydro has to go.
(if your considering the pulley swap...)
Does your JD have an electric clutch for mowing? If not, is the top pulley smaller than the bottom? On most hydros they're not. But I have a JD with a hydro that does. So if yours has a small top pulley, try flipping it upside down (you may need a new belt). If it has two big ones, then you need to buy a 6" pulley for it.
I know that is a lot of information, but that's the simplest way to do it. Remember, don't care for it, don't ride on it.