The answer is two-fold: it is a combination of weight distribution and which wheels control the vehicle motion.
Most front wheel drive cars have their engine mounted transversely. Picture a solid line running from one front wheel to the other. The engine is then turned sideways (the long way) across that line. More of the weight is on that line, applying more direct pressure to the front wheels and tires. Even if the engine is not transversely mounted, it is still in the front.
Also, the transaxle makes the front end even heavier. In simple terms, a transaxle is the FWD transmission and axle unit that is mounted on the engine and connects to the front drive wheels. This takes weight from the middle/rear of the car and mounts it on the front wheels.
So, why is all this extra weight good? It presses the wheels and tires onto the ground for better grip on the slippery surface. It just happens, that on FWD, these same wheels are moving the car forward or back and steering the car.
With the bulk of weight and control in the front, this gives FWD a natural bias toward better handling than RWD counterparts.
As for your question about putting RWD in reverse, it would not work the same since the weight bias is different.