Carving can be quite tricky to do as it depends on the terrain you are trying to do it on. You need to either hold the or and pull back on the and move the in the direction you want to carve. You will also need a great deal of speed for this to count. You will know if you have pulled off a successful carve as "Carve Bonus" will be displayed at the bottom of the screen.
Make sure you pull the directional stick in the direction of which trigger you are holding. If you try to carve by pulling left and hold the you will not carve the snow.