Since the extension cord contained both the hot and neutral leads, and possibly also a ground, the electric field produced would be very limited in size. Ten diameters of the cord end connector away and the voltage differential in the water would be very small.
On the other hand, dropping just the live wire into the water without any return path nearby could produce a fatal potential difference for several times the depth of the water (or the distance to a large grounded surface) away from the wire. You have to look at what voltage distribution the electrode(s) would produce in a uniform resistance conductive material. The potential difference is what will induce fatal currents through the salt-water electrolyte of the body. In water whose salt content is comparable to the body's electrolyte conductivity the effect would be somewhat reduced, since the body would provide less of a preferred path. But any current which would have flowed through the corresponding volume of water will pass through the body instead.
For understanding what is happening, the math of the soil potential around a ground rod is very similar to the case of a single electrode in the lake.
When you drop a hair dryer into a bathtub, the effect is made worse than the cord end case because there is a larger area of exposed wire attached to the hot side of the circuit compared to the ground side of the circuit, and the grounded metal in the tub is also proportionally closer.
Nicely put, the problem is many do not think in three dimensions and all the parallel paths that a large three dimensional conductive body whether it be soil or water has, the larger the area and amount of water/soil the more parallel paths there is, and after a short distance away from the injection point there are more parallel paths that connect to the Earth then there is in the small amount of water/Earth around the injection point, it is this small amount of parallel paths around the injection point where the almost all the voltage from the injection point is dropped and can have the highest voltage difference of potential, this area from this point out to the point of where the voltage is no longer able to be detected is called the "Sphere Of Influence" in Earth/soil this SOI in 100 ohm per CM soil would be about 26' in water like was said it depends heavily upon how conductive the water is, and can be much larger, the more conductive the water is the smaller the SOI, the less conductive it is the larger the SOI so the more conductive the water is the higher the voltage drop is in a very short distance from the injection point and the more voltage across your body if you are in this area close to the POI (Point of Injection), in water that is less conductive your body will receive less voltage across it, unless you are very close to the POI where the voltage drop is the highest, but remember being immersed in water it doesn't take a very high voltage to cause you big problems.
It can be very confusing trying to think about a three dimensional view of this and while many try to think that the current will take a single line path between two points because we are use to thinking of current travailing in a wire, it doesn't work like this as current takes all paths proportionally to the impedance of the parallel paths, lets say we have salt water, you would think the voltage could travel much farther from the injection point, but because of the fact you have more and more parallel paths back to Earth as you get away from the injection point, that have a much higher ability to keep the water at the same potential of Earth at a much shorter distance from the injection point, so in just a few feet you would have the 120 volts across two points, now get in between these two points and that voltage will be applied across you, now with fresh water that is not nearly as conductive the same 120 volt drop can be across an area 60' out from the point of injection or more, since this voltage drop will be a compound drop as the shells around the injection site have more and more amount of water as you get farther and farther away from the injecting point but very little amount of water in close to the injection point , which basically means the voltage that will be across you body closer to the rod can be more then the voltage will be as you move out from the rod till you get to the outside point of the SOI, and much math would have to be done to figure out how much with knowing how conductive the water is, in the form of ohms per CM of water.
Now here is what makes the fact why electricity and water so dangerous, being immersed in water it takes very little voltage to start causing you problems, I seen a list, where even 1 volt can cause you to be very uncomfortable, 3-5 volts and you can no longer pull yourself out of the water or in some cases even swim, get much higher then that and well you can very easily drown, I think it was around 10-20 volts that your heart go into fib when immersed in water, now why does it have this effect when your immersed in water, it goes back to the many parallel paths that is connected to your body which is now wholly connected as part of the conductor.
So I wouldn't go around throwing extension cords in water where people are swimming.