A rail vehicle has a vehicle body supported in a sprung fashion on bogies. A snow plow has two blade plates that run to a point and a plow blade arranged vertically adjustably behind the blade plates. A projecting portion of the plow blade that projects downwards beyond a lower edge of the blade plates is adjustable. The blade plates rest with their lower edge on a base plate which forms a cutting edge that protrudes from the lower edge in the direction of travel. The snow plow is attached to an under frame of the vehicle body such that the base plate maintains a safety distance from the travel rails. The safety distance is predefined by a maximum spring compression of the vehicle body. The protruding portion of the plow blade is set as a function of the safety distance and of a wear of the wheels of the bogies.