It depends on what kinds of farm animals, and how many. Most of the zoning emphasizes horses, since they are the most popular large animal that people keep, and the MLS even has a checkbox for horse-zoned proeprty. The number of horses allowed is different in Las Vegas, North Las Vegas, and Clark County based on lot size. Horses can be kept on property zoned RE, or its equivalent. It is common to see a goat with horses in the RE areas as a companion animal.
Cattle are usually restricted to RU zoned land (or its equivalent), of which there is less and less.
A chicken or two, probably no problem; a whole flock of chickens, better have the right zoning.
Probably the best thing for you to do is determine what kind of farm animal you want, and how many. Then check with the zoning offices of the various entities:
N. Las Vegas (702) 633-1537
Las Vegas (702) 386-9108
Clark County: (702) 455-4314
Mike Pristow, Donna Hodge & Associates
Keller Williams Realty