Glad someone brought it up, most compact utility tractor electrical systems won't take kindly to a winch. They are usually pretty small as they only need to feed some lights and gauges. You have a large capacity battery to deal with a large diesel starter and engine compression, but a winch under load will quiclky run the battery flat. That little alternator wasn't designed to charge a dead battery, only maintain a healthy battery at peak charge, recover from startup loads and power the accessories. It will take it a LONG time at idle RPM to recover a dead battery, with it's regulator working it at 100% output the whole time. It wasn't designed to run at 100% output for extended periods. If you don't get the battery recharged and shut down too early, Then you are stuck and the battery has no power to restart the tractor engine.
As mentioned, Big difference between pulling a rolling 4000# and trying to drag/lift 4000# out of the mud. figure out your all up weight and goto a good 4X4 shop and ask them what size winch they would reccomend to get that weight vehicle out of a good mud hole. A 4000# vehicle would probably be reccomended to have a 8-12K# winch. Then ask them what kind of an electrical system is required to feed that size winch reliably.
The only way I would want to try and pull from the FEL would be straight ahead. It is a Loader, it was designed to lift and wasn't really designed for side loads. As I am sure you are aware, it is usually difficult to find an attach point to pull from directly ahead. Also if the bucket is at any height, you have a lever arm that will be above the CG and a off angle pull could pull your tractor over on it's side. I think the FEL is better used to dig in and push with the bucket curl when you are stuck.
I think you would be better served with prepping some short lengths of chain that can pass thru the rear wheel and around the tire. To that chain you attach a longer chain or cable back to an anchor point. By putting the tractor in low low range and locking the rear differential, the wheel will act like a winch drum and the tractor tire/wheel will roll back up the chain dragging the tractor behind it. This of course only works well backward.
If you are getting stuck routinely enough to need a winch, perhaps you have the wrong tool for the job/terrain.
Ron