OP, if you have a 24V winch and a couple of "12V" batteries, you don't need an inverter for the winch. You can just connect the winch to the 2 batteries wired in series. That should work fine, with appropriate cables and switches. Except for the need to recharge the batteries after each use, which you would then need to do one at a time if you only have a "12V" alternator. Bit of a pain. And yes, 12,000 lbs is overkill for most routine loading jobs I would think. You would have to find out how much pulling power you really will need.
If you don't need 12,000lbs, an alternative if you can use the winch for something else or sell it for lotsa bucks, might be to use a smaller 12V winch which would be easier to recharge a battery for. Maybe around 2000lbs if that's enough for you? Those are pretty inexpensive.
Or even use a 120V AC winch. Also inexpensive if smallish. One around 2000 lbs would probably have something like a 1HP motor and draw maybe 10A so a common 2000W portable generator would be able to handle that probably, which would be very convenient if you have other needs for AC, with no need to worry about batteries etc. Assuming you already have a generator, cuz the good ones aren't cheap.
Keep also in mind that unless you can have the alternator keep up with the winch, you should ideally get a deep cycle or dual purpose battery, as a regular starting battery won't like too much the deep discharge the winch might cause. If you use the winch a lot, the battery life might be significantly reduced.
