There is always a risk when dealing with horses. They are
animals, and can therefore be unpredictable. The best thing you can do is minimize the risk. ALWAYS wear a helmet when mounted (or even on the ground if your dealing with a rank or problem horse, but since you're fairly new to horses, I doubt that that's your situation
). Keep an eye on the horse, especially the ears, when working with/around it, and be familiar with their body language and what they're "telling" you. Don't wrap a lead rope around your hand, hold it loosley coiled. Just little things, common sense. Accidents can always happen, but by thinking through the worst case scenario of the results of your actions and acting accordingly, you can minimize the risk and a habit of safety becomes second nature.
That's rough that that girl lost her teeth getting kicked, I hope she's okay. But, to put things in perspective and to try to put your mind at ease, I know a girl who's been into horses for years, jumping and showing, who knocked half her teeth out on a waterslide, no horses for miles. Accidents happen, all you can do is be as safe as practically possible.
Hope that helped, and I'm sure others can add little tips to the list I gave.