I recently noticed a 3" cut in the rubber (between lugs) running across the width of the tire. This cut in not very deep and the tire is not losing air. Is the tire safe to use or should I replace it?

 

Tires often get these "slits" from everyday use over common terrain. If it holds air oven time and it is not too deep I would not worry about it. If we were talking about a vehicle used at high speeds with quite a bit of pressure in the tires, such as automobiles, that would be different. But with the relatively low speeds and low tire pressures of ATV's you are in no danger.