It is low, low impact. However, saying you won't fall (especially in the learning stage) isn't exactly true. I am a good intermediate level skier, classic style. I am not fast, fast, but I can climb like crazy and the fear I have of downhills in cycling is not there when I ski. I love x country skiing, almost more than riding, because I don't get to do it as much. However, I skied on beginner trails for like 15 years, because I was too afraid of big falls or descending. It only took a couple of trips with our cycling friends, and I was out on the blue trails. You will fall in the beginning, just getting the coordination down. Sometimes, you fall climbing, when an edge slips out, but that's more like a knee or thigh down. Not a big fall. Obviously, you can fall more descending, but you can also learn to control your speed on skinny skis! I hardly fall at all, now and when I do, it's usually when i am climbing, tired, and my position gets out of whack.
And, falling on snow is much less scary than falling on the road or trail.
Go for it, Catrin.