I run a very cheap Smitty winch that I won at some promotional drawing at 4wheelparts in Nashville. While the winch was free, I spent more than what it would have cost to buy prepping and wiring it up.
One thing that concerns me with your setup is you are doing what is called remote mounting the controller box. Most winches are intended for that box to attach directly on top the winch itself, and depending on the mounting spot that may or may not be a great idea. In my case I had 2 reasons to remote mount mine, one was I didn't have room, and 2 was winch controllers are sensitive, and being down in the mud will cause a lot of corrosion and then they don't work when you need them. Mine is high and dry up by my firewall.
But there is this thing called voltage drop. DC is prone to loose voltage as you increase the length of the cable. 2AWG might be just fine for the 6" of cable you need when the box is perched on top the winch, but you added at least 5' to the setup, more like 10' as it's out and back. (Third cable doesn't count as you only use 2 at a time, cable in or out....)
Now when you cheap out on cable it's usually by going too small. Here is what happens, you starve the winch for power. Best case the voltage drops and the winch just doesn't pull like it should. You have an 8000lb winch that can only pull 3000lbs or some such. (Rough example) Worst case your cables see the winch motor engaging as a dead short, heat up, and burn your truck to the ground.
Hence why I run 00 (sometimes expressed as 2/0) cable on my winch set up very similarly to what you outlined your plans are.
So to answer your original question, in my opinion, the wire you posted is not adequate. Mostly because of it's gauge.
There is a quality to wire called
ampacity. Simply put, it's how much current a wire can handle without getting hot. By and large, in my situation it turned out easier to shoot for that than figuring out voltage drop, odds are at the sized involved, if it can handle the current it can handle the voltage drop as well, especially at the amps and distance runs for a winch. Doing the math could get convoluted, but as a rough guide in the real world, it should get you close. Welding cable usually has ampacity specified thus making it handy, and winches and welders are in the same high amp ballpark.
According to the chart in my winch's manual, (yours may differ) at max pull (8000lbs) the motor current is 410 Amps. So in my case I sized the wire to handle the amps. As you see in the chart below for up to 50' @ 450 amps, 2/0 is suggested. Since my run was well under 50' and just under 450 amps, I chose that as the size I needed thinking it would supply the winch at full pull with some safety to spare. As a general rule with wiring it's better to err on the larger side than smaller. Not to say smaller woulden't work, but do it this way and you can feel pretty confident it's adequate.
Given 2/0 wire, calculating my voltage drop came up acceptable. 2/0 is big enough, larger still would be ridiculous. Click below and you'll see I loose about 3.2% at full pull. Mind you pulls less than 410 amps cause less drop, so a 2000lb pull @ 195 Amps would only cause about a 1.5% drop.
Also factor in with the engine running your alternator will be assisting in getting the voltage above the default assumed 12v of the battery alone, to more like 14v, which will further work in your favor to reduce voltage drop, and the maximum drop on a full pull is more like 1.3%. So in this case, wire sized to comfortably handle the amps seems to take care of voltage drop also.
Numbers from voltage drop calculated here: (Note depending on the calculator you use, results seem to vary...I'd consider it a rough guide.)
This free voltage drop calculator estimates the voltage drop of an electrical circuit based on the wire size, distance, and anticipated load current.
www.calculator.net
And if you are cussing me for thinking of all this over a stupid winch install, remember I have to live with myself and yes I overthink everything to this degree. Sometimes it ain't very fun.
