It's not an uncommon sight to see a snapped winch line. This normally is due to abrasion, cuts and knots, lack of maintenance but most commonly from emergency misused towing and failed kinetic style recoveries. It is a sure thing to damage a rope by using it in a way that puts shock into the line, point loading it in ways it was not intended for. 

UHMWPE based ropes have as little as 3% or less stretch in them depending if they have been pre-stretched so if you intend on shock loading them go for a rope that is 6-10+ times the rated size for your vehicle. So learning to do the 12-strand loop eye splice is a good tool in the knowledge tank. A snapped rope with a new loop end will happily bounce back to 100% strength given there is no other damage to the line and is easy to do once you know.

The only tools needed is a knife/scissors, tape and a splice tool of the correct line diameter. If you don't have one of these handy (and lets face it you probably never will), the next best thing is a large sewing needle and tape or something long and thiner then the diameter of your rope. For example you can use a branch with a pointed cut tip and just tape the rope to the end to get the inner splice done correctly. With enough