We use a wire winder that has its own 5.5hp Briggs & Stratton engine. It is called the EZ barbwire roller and came out of Texas. It cost $798 new.
You can wind wire into the back of a pickup or a flatbed if you tie the darn thing down.
It rolls 1/2 mile of single strand wire into a roll. If you are just getting rid of fencing, it will wind up to 5 or 6 wires, obviously not more than a few hundred yards.
I can't imagine needing tractor power to wind wire unless you are doing something special.
Last year when the railroad replaced their fences, the contractor just took a small tractor - about 40 hp - and started doubling the wires up all at once. It ended up about 300 feet long and was about a foot in diameter. If you have a gulch to put it in, it ok. I think it was gone the last time I went by so they did something with it.