Interesting question -- especially after I had ski patrol greet me by name outside the first aid station last year after daughter no. 2 (8 yrs old then) failed to show at our rendezvous point. An awful, sinking feeling, especially having to explain it to my non-skiing wife. 25 stitches later (on my daughter, that is) everyone was fine.
So how old? I don't know -- but it depends more on child's skill and responsibility level than calendar age. Was it a mistake at 8? Probably so, but that was a function of her skill level. Also lousy conditions -- she hit a dirt patch in thin snow in March -- more bad judgment on my part to take kids out in that. At least she had the presence of mind to get help herself, but only after getting herself back up and skiing two more runs before noticing the blood through her ski pants.
And yet, this year I let her ski free with her twin brother, 12-yr old sister and their friends on the small areas we ski. With more precautions than last year. And a lot more skills ... after @10 days skiing over this winter, with lessons on 4 days, the instructors put the girls at level 6 or 7, and the boy is at level 5.
Same precautions generally as previous posters though I don't have the dog tags/bracelets. That's a great idea Tanglefoot, any clue where to get them?
Other precautions/routines that we use:
-- Buddy system. "Skiing on your own" means skiing without a grownup -- but kids have to stick together in pairs.
-- Depending on conditions and terrain, definite limits. Usually no grownups, no black diamonds. That will change over time.
-- FRS radios. Yeah, they're annoying, especially when kids misuse them. But, after another incident earlier this year, I wouldn't take a family group skiing without them. Same daughter knocked her wind out and twisted up in a fall where bindings did not release, right in front of a ski patroller (just like the post that started this all...), so he put her in a sled and we went way offsite for X-rays. I had no way to communicate real time with the other two kids who were then REALLY left alone skiing, I was away for hours. An added benefit to these radios is even if you're not w/the kids, you can overhear their chatter and have a general sense where they are, how they're doing.
Separate from these details -- why let them ski alone at this age?
First, we like to ski together, but after a while, it's not fun. And if it isn't fun, they're not going to like skiing, which is the whole point here.
Second, they don't get much freedom in their life -- very little goofing off, hanging out at the playground after school, taking off at 9 a.m. on a Saturday on bikes and coming home for dinner. Seems like more of that when I was a kid, but not possible for my kids, and many others, these days. So, if they can run free for half a day at a little 100-acre ski area, ride the lifts, buy candy bars, that's a good thing. And in the process, they use their own judgment instead of asking me what's OK all the time.