I had a similar accident to your second one. I hit a curb with a wheel after trying to turn on an icy intersection. You should probably do an alignment check because my car alignment was completely off. As for your first episode, if you added more throttle, you would avoid the slide. But as always, it is easier said than done. In such situations, it is very scary, and the first instinct is to press brakes, which only makes things worse in the winter time.