Depending on the year of your Suburban and if it was spec'ed out with a tow set up, you should already have the #10 wire in your harness. It will be near the drivers side fire wall, engine side, below the power distribution box. It is an orange wire and it has a terminal on it for connecting to the hot stud on your power distribution box. It should also have a similar blue wire near it, the one used for the electric trailer brakes.
At the back end, the orange wire will be wrapped up near the end of the harness. You can feel the lumpyness of wire under the tape, inside the frame, on the drivers side. That orange wire is for your trailer hot. You'll have to provide the #10 wire from your connector ( I use a seven pin Pollack plug ) to your winch battery.
Lucky for me, I have the camper option on my Crew Cab. So from the secondary battery ( amongst other things connected to it ) I run, through a disconnect, some #2 wire down the frame and to a quick terminal attached under my rear bumper. My winch has about 2 feet of #2 wire lead with a mating quick connect so I can plug in or unplug my winch at any time. I usually keep those wires dead by turning the disconnect off when not in use. Most of this material I got from McMaster.
