Stance training is about transitions and leg strength. A good example is when performing an over the hip throw the first thing is to close the distance, turn into your opponent, drop your weight. Using a variation of a horse stance to drop is the key, because without this you will not be able to uproot your opponent's balance.
As for fighting out of a horse stance (striking), unless your fighting someone who is a complete newb it is a dangerous and pretty stupid thing to do. Good strikers use circling, fight at angles, are are light and comfortable on thier feet, not rooted down and moving at the speed of a pregnant yak.
"The hero and the coward both feel the same thing, but the hero projects his fear onto his opponent while the coward runs. 'Fear'. It's the same thing, but it's what you do with it that matters". -Cus D'Amato