The wide prong, on a 110V circuit, or as I called it the 'neutral' wire, is the common, on the 4 prong plug. Maybe I should have phrased it better, but most people know a 110V circuit as being wired hot, neutral, and ground.
The common, and the ground, will usually wind up at the same point in the breaker box, (which is why it will work that way) but as you stated, the 'ground' wire, is for safety purposes only.
The reason I mentioned it 'would work' either way, was so whoever hooked it up, would be sure to double check the ground circuit, and not just assume that because everything 'worked' that it was to code and 100% safe.
I maybe should have clarified that better.
If I were running the winch, I'd run a separate ground wire, even if I were using the conduit as a ground, because I can see where a winch can 'pull loose' from where it sits, and pull the conduit apart, taking away the ground circuit.
I will take this thread a different direction. One concern I have with your proposed wiring is the use of a #2 AWG cord in this circuit. If the welder circuit has a 30 Amp breaker and part of the circuit is #12 AWG wire, don't we have a problem? I thought #12 AWG wire is rated maximum of 20 Amps and what will happen when an overload of 28 Amps occurs? A fire in the #12 AWG wire since the circuit breaker won't trip?
Most of us have too much invested in our shop to risk losing it all because of shortcuts.