I say do it man, I started on skiis when I was 3, by the time I was 6 I was bombing down single black diamonds, by 8 I was getting silly and ducking ropes and whatnot. Was talking with my dad after getting back on the snow for the first time in a few years, and he said he really had thought about selling the business and moving to Colorado back then. He told me he wished he would have seeing how happy I am on a mountain and knowing how I used to kill it on snow as a kid. I didn't know what fear was back then, my mind and body was ripe for learning the sport. Unfortunately at most of the resorts we went to boarding wasn't allowed as it wasn't mainstream then and I didn't pick up a stick until I was 14 or so.
Anyways, you've got nothing to lose but a few hundred bucks, your boy has a passion to gain from it. Like someone above said make him earn it through extra chores and whatnot around the house. I remember when I worked my ass off with my dad during a summer to earn 600 bucks and bought my first dirtbike, an old 4 stroke 80 woods bike. That was the year I learned what fear was, broke my damn collar bone on the thing, but loved every minute of it and was back on it before I completely healed up haha. Point is, your son is enjoying the sport, embrace it.