Jackson Hole *does* have a snowcat operation. They ski Angle Mountain, which is near Togwotee Lodge (pronounced TOW-guh-tee) Lodge, about 45 miles northeast of Jackson. I haven't done their snowcat skiing, but I have skinned up and skied Angle a few times. It's wonderful, varied terrain and I've always had a blast when I've gone there.
The snowcat skiing at Targhee is great fun. There's not much "terrifying" terrain, but it can be really good skiing.
Here's the website for the Togwotee operation:http://www.jacksonhole.com/ad.page.asp?nodeId=133