I want to do the same thing. In fact have the same winch just 20 years older. There have been discussions here about the tractor alternator being not big enough to handle the winch.
I was thinking about a marine deep draw battery , maybe a type 31, and just charge it up in the barn. I was thinking about mounting the winch and the battery box on a carry all and then adding the chain grabbers to the carry all as well. Weld a wedge of some sort on the bottom of the carry all to act as a brake. Plus a box for all the cahin saw stuff. Evry time I put that stuff in the bucket I forget and dump it and then run over it. Also I was thinking of changing the wire cable to this stuff.
Amsteel Blue, Winch Line, Rope, ATV winch lines
I got the carry all. One of the issue with my winch is it has no reverse, just free wheels out. If the cable capsizes on the drum it has to be hooked up to some thing and the vehicle drive away to unspool it. I think when all is said and done a 3 pt logging winch would be better but they now cost over 3k. Still thinking.