It's probably more winch than the tractor was designed for, what's the horsepower requirements for the winch? It'll probably work fine as far as the pulling part is concerned, just don't expect to pull the full 9000 pounds the winch is rated for if you need more than 30 odd HP at the PTO. I suspect the full capacity will require 45-50 + HP to achieve.
Where you won't like it is when you try to lift a load of logs attached to the winch to haul them out. I have an
L3400 and a Norse 290 winch, which weighs just over 300 lbs and has a hauling capacity of roughly 7000 lbs.
Your
L3800 has the same lift capacity at the 3-point as my
L3400 does. I've had quite a few situations with a load of hardwood logs attached to the winch and the tractor can't lift it.. or can only pick it up a foot or so. You have to drop a few logs and make a second trip. That would be worse with the heavier winch, about 400-500 lbs less payload.
The extra weight of the bigger winch takes away from the payload capacity of the tractor, is what I'm saying.
My 290 was new to me, the previous owner had bought it and never used it, it was still strapped to the shipping pallet. Unless you're getting a super deal on the FX-90, I think I'd pass. If the price is really good, you can try it for a bit. If it doesn't work well for you, I doubt you'll lose much if you decide to sell it and go smaller.
Sean