Vicky, don't be so hard on yourself! The reason you don't see people carving is partially because it's not easy. If the terrain is hard and granular, it can be really hard to carve. I don't think the surface was 'icy' on that day (ice patches are kind of dark), but it's hard to tell from a video.
Similarly, if it's too powdery, the loose snow gives away under your board, so you're usually floating. It's also harder to carve on bumpy, ungroomed terrain, but it looks like the run you were on was groomed corduroy.
If you watch this video: CASI Level 2 Standards 2010 - YouTube
, you will see some *really* good people carving. Notice how their board turns relatively gradually, and the board spend more time pointed downhill. Now compare to your video... you're kind of sharply turning the board one direction, then another. The board is kind of being flipped left and right rather than being ridden on the edge, and it spends little time pointed downhill.
In the carving video, watch how the snowboarders really get their board on an edge, and let the edge guide their direction. Watch their knees and posture...
But really, don't be so hard on yourself. Carving is an intermediate/advanced skill, and it's an aggressive way of riding down runs. It's kind of a finesse skill though... like the 'proper' way of using eating utensils. Don't get too caught up in being 'proper' if it ruins your fun. As you probably noticed, a lot of people *don't* carve.
That said, carving is *amazing* fun. It's best to try it on green terrain that you feel comfortable taking aggressively, and once you get it, try moving it to blues.