There are several ways to exceed the capacity of a wet (or, for that matter, dry) "friction circle"... Steering, braking and accelerating are three of them. All else being equal (i.e., given identical tires, road conditions and throttle), a more powerful car will accelerate faster and therefore hydroplane more quickly than a less powerful car. (I'm not sure if modern ABS systems make "more powerful brakes" irrelevant in this regard.) Actually, even a car with faster steering response will hydroplane more quickly than one with slow steering response, given an identical amount of wheel-turn
You seem to be referring to the ability of a powerful car to break its tires loose. That's all true, you can do that by accelerating fast or fast steering inputs. But this is skidding not hydroplaning, and it can be done on any surface. Hydroplaning is the inability of the tire of removing the water it rolls over, the tire cannot handle the amount of water and begins to skip or float over it. Once the tire floats on top of the puddle, ABS , stalibilty control, etc become useless. A good wet tire will use the deep grooves and lateral channels to remove the water it rolls over, 4,5 6 gallons per second for ex. The more gallons removed, the better the tire. As speed increases, all tires will eventually be overwhelmed by the water and will hydroplane.
The trick is to keep the car under that limit. So let's say you have a summer tire that will start hydroplaning at 75 mph. Assuming equal weight, an M3 and a 316 will both start hydroplaning at 75, regardless of their horsepower. The only difference will be that the M3 can reach that limit sooner than the 316.