As always, there are good comments mentionned above.
I will give my experience with my daughter Morgane who started skiing (more like sliding on ski) when she was 2.5 yrs (30 months). First of all, I didn't expect to start her so soon, but after seeing me and her mom go skiing, she really wanted to join in the fun before the season was over.
That first time and only time out before she turned 3 in October was at Edelweiss. We did maybe 2 hours of skiing. The method used was between our legs. Yes, Jim is right, it's definately very hard on the back, especially when I had a back injuring two months earlier. At that age with the spring conditions, her legs were definately not strong enough to ski, support her body and stand (this might not be the case with other kids in other conditions). The goal here was not to teach her to ski, but more to let her experience the fun of sliding on snow like her parents loved doing.
Ryan, I read our comment regarding this method. I agree that it could be dangerous. However, like all the stuff I do when I ski, I evaluate the danger based on my abilities. In this case, the odds of me crossing my skis with my daughter were relatively low. I had 201, not in a full snowplow position and not 100% of my daughter weight were on her skis. But I do definately see the danger in it.
The next season, my daughter was 3 and skiied 8 times. First time out (2 hours) was between the legs(?) and/or with my ski poles used as a harness. The next 7 times was with a harness. The tip of her skis were connected to each other with a velcro strap. The harness was also more related for a safety reason. Of course I used the harness to slow her down when needed, but also a few times to stop her dead in her tracks when someone cut her off or feel in front of her.
When she was 4, she also skied 8 times. I believe that most of that year she skied without a harness. She could edge a turn, control her speed, etc. Ski most beginner runs without any difficulty most of the time.
At 5, we got her register in ski lesson. 8 times again. Why? Because we wanted to assure us that we took the time to go skiing with her, she just had a baby sister. Also because she knew how to turn and control her speed, but didn't necessarly want to listen to her dad. So being with an instructor with other kids her age would help.
Last year at 6, she got the ski bug. She skied 17 times. At the end of the season, she could ski any intermediate runs and a few black diamond ones. Her favorite place, that one visit at Mad River Glen.
Now she's 7 and judging by the way she skied on satuday (not really parrallel yet, but the speed and confidence is there), I am sure that in a few years...I will be trying to kept up with her. Especially when she said she would like to race.
Not a good thing for those parents that do not want to ski in the same small areas all Winter, at least with the lesson, I am only a prison for 8 Saturdays.
In summary, if you want to get your kid ouside and have fun, regardless of her skiing skills, you can get her on ski at 2yr. However, I remember reading maybe 10 yrs ago, that for the abilities and skills, the skier that starts at 6yr is not going to be disavantage to those you started at a much younger age. The progress curve is greatest around 6-7, regardless of when they started.
There is a couple of stories about age. Skiing at Whiteface when my daughter was at the daycare, there was a kid that was more or less the same age as my daughter (ie. 15 months) and skiing. I believe both parents were ski instructors.
Second story is (hope, for the aging skiers going downhill). The first race I did Master race, John Fripp (82?) (aka same as the name run at Tremblant, ski school director in the 1940s before Ernie McCulloch) beat some much younger guys. Remember the joking with his son (late 40s), that if he wanted to ski like that one day, he better stop smoking in the starting gate and start training.