If you were to run them underside, I'd make sure to use split loom, and a load of p-clamps, zipties only where it supplemented keeping the cable sucked TIGHT.
But really the safest way would be to keep as much of the run in the cab, both for protection & as mentioned, you could have a junction in a quarterpanel, then from there route out through a hole you use a good rubber grommet so as not to chafe the cable or even loom over time on a sharp metal edge where you drilled a hole.
I'd want a fuse/switch/ring-terminal & wingnut- close to the battery, one I could EASILY access to pull & only install / energize when I wanted to use it if I were to run the cable fully the underside of the body. That way the line was only 'hot' when needed. One stray stick or such poked up, a good rock or whatever could really mess up the works, not to mention replacement cable time & lack of use if needed.
If it were my 80 & my project, it would travel to the rear inside the cabin, and even then I'd have it secured the route it took, not just laid under the carpet - at a minimum in my 80 positive would have split loom where feet contact that section(s), and some of the zipties that have a loop head you can either use existing hardware to secure to (I avoid self-tappers, good for stereo shops, not for long term owners)-or ziptie that loop to something. As a guard for foot traffic those soundproofing sheets cut into ~6" wide strips & laid over cable in split loom are good, and it isn't dead permanent, you can still gain access (did this in a car I remote mounted the battery in the trunk) and the carpet just tapers laid over those sheets.
-Main point being a pack of ~20 loophead zipties would be in my install kit. They're just useful, once you get some you'll start finding all sorts of uses.
Something else to consider is if you have a CB antenna mounted out back anywhere, you need to keep that power cord as far away from that antenna line for interference.
If this is just for a rear winch & nothing more, I'd not even have it hardwired permanently - I'd just have one of those pigtail sockets (Blue Sea makes one, same thing some use as the socket to their jumpercables) -with a fuse wired in the battery area, and pre-plan a route to lay the winch line (you'd need to extend lines obviously, if this idea seems viable for you) -through the cab & maybe out a rear slider window on down to the receiver area (guessing you are talking a temp receiver mount winch setup, maybe even a receiver mount up front?)
Bonus of that socket is to make a set of jumper cables with socket 1 end / clamps on the other - nobody can walk with your cables if you help them out. 2-fer-1 use out of that socket.
@NLXTACY has a socket like I'm talking IIRC - does the jumper cable thing off his. Maybe he can chime in & either confirm or LYK I'm smoking some good stuff?!?
But then again, I tend to the train of thought that "anything worth doing is worth overdoing". Just no bare bones under-guaged cable, 10 zipties & no fuse routing it undercarriage!