Poor Cows

Sorry, that's not quite right.

Between two points in an electric field there is always voltage.
The more distance between the two points, the greater the voltage. Between the forelegs and hindlegs of cows is a pretty big distance; accordingly, the resulting voltage is quite high, too. Because of this, a strong electric current flows through the cows' bodies which leads to severe injuries.

In the picture you can see that the cow stands with its forelegs on one particular potential niveau; the hindlegs, however, stand on a different niveau. This difference in niveaus is the reason for the high and dangerous voltage.