Im sure you "could" get away with 1/4, but is it worth the risk?
Safety is never something worth skimping on. Its worth the extra few bucks to ensure that you wont snap a cable when you need it most. Just because the rope itself poses little threat when it breaks, doesnt mean that nothing bad will come if it does. You could be winching over a rock obstacle, or steep hillclimb, be out of the vehicle, and the cable breaks. Bad situation. Go with the 5/16" or better. Just my opinion.