Some good advice on this thread. I think the need for a powered saw depends on how much you anticipate cutting in a short period of time. If you foresee situations where you're going to cut a lot of stuff and you are in a hurry, then a powered saw is probably what would work best. Once you're certain you need a powered saw, the main options seem to be:
1. Gasoline. Common, tried and true, and for the cutting efficiency probably the cheapest. Biggest cons seem to noise, smell, explosive fuel, and they may not sit for long periods of neglect unless you put them to bed well. If you envision rare episodes of heavy cutting and you don't like the other cons (they are personal preference sorts of things) then you could consider:
2. 110v corded saw. Won't cut like a powerful gasoline saw, but will cut pretty large stuff well, as long as you get a good saw, high amperage cord, inverter large enough to power it, and you can tolerate the damn cord. It can remain unused for years and work as well as the day you put it down (just don't leave it in the rain). If you're clearing a track with a lot of cutting as you move along with your vehicle the cord seems to show an inordinate affection for the space between your front tires and the ground. Oh, and it might not be a good idea to stand in a puddle while cutting merrily away....
3. High quality lithium battery saw. I did a lot of research into these when I was convinced that I needed one. If you want a chain saw because you're going to cut a lot of larger stuff, the expense of a good saw, multiple batteries, a fast charger, etc. adds up quickly. I gave up the dream when I realized the setup I though I'd need would run close to $800 or more.
Indecision left us without a powered saw. On the other hand we've done fine without it via a combination of axes, pruning style saws, bow saws, a winch, driving over/around, and turning back (shame). But, we haven't cleared a road through a forest in the early spring, or a long overgrown track in Australia by hand. Those are the accounts I've read where a powered saw seemed to make the difference between getting through and turning back. At any rate, getting back to the original question - I don't think there is an adequate 12v corded saw available. The most similar animal would be the battery powered saw, multiple batteries, and a fast charger.
Howard
