Thanks for all the responses so far!
I know how much my 20 foot chain weighs and the idea of using 100 feet of chain seems like it would be a real workout. Dealing with logs and chainsaws is already a pretty good workout, I don't really need more. I was not aware of logging ropes, perhaps I'll look into that further, if anyone has suggestions or links please post.
I considered an electric winch, the price is not too bad, however then you need a mounting setup, another battery, cables, etc. I looked at one 8000 lb winch and it was rated at 500 Amps of current at 8000 lbs of pull, that would deplete a battery pretty fast. Perhaps get a portable power generator to charge the battery and ......
Since the tractor has hydraulics and a pto it makes sense to use that, although I'm not aware of any affordable hydraulic/pto winches. Any suggestions for those?
I agree that a real logging winch would be the way to go. A couple of you with logging winches mentioned buying one, using it for a while and then selling, however I think that if I were to get one I'd keep it for a long time.