i'm a newbie to carving and what i found out that really really helped my heelside is to put a cant on your rear foot. This was suggested to me by a few people. This helped force my rear knee more into the heelside turn, which forces the board's edge in. Plus, as mentioned above, it kept me from applying too much force directly down onto the board.
Its frustrating but well worth the effort. I remeber my first day when I was able to confidently link all my turns together and see my tracks all over the trails. I was in heaven:D
edit: as cb200 said, don't reach for the snow at all. That will come with time. Also, i was told by many people that draging your hand in the snow can be a bad habit because you can twist your elbow/shoulder if you hit some ice chunks, aka death cookies.