I thought it might be interesting to add that in some semi-desertique areas, cats are domesticated for their specific ability to hunt and catch scorpions,(which are a real danger). They are also known to hunt spiders (some of them are really dangerous where I used to live) and small snakes... I have never seen a cat catch a snake really... but for scorpions and spiders it's a really common sight. I know that we are not here to make a full list of the 100 species a cat can hunt but I thought that those where quite relevant since they are an incentive to keep cats in some regions.
I once saw an animal documentary in which an orange desert cat, which by the way looked a lot like a domestic cat, killed a rather large poisonous snake by using its incredible speed to claw it without getting bitten, so yes I believe it's possible to train a domestic cat to kill snakes.
I've owned plenty of cats that killed rattlesnakes. One method of hunting is to be fast, as previously noted. The second is to be patient and wait for the snake to try to escape and striking while it is uncoiled and unable to mount much of a defense. Pretty much any animal less than forty pounds is fair game to a sufficiently motivated cat.
I'd love to hear some opinions on this.