It's a personality thing. You're the best judge of your child but even then it is still hard to say!
We put our oldest two, then 6 and 4, in ski school (plus afternoon creche for the 4 year old) and they were absolutely fine. No wobbles, and they improved so much beyond where they had got in their fortnightly lessons at Hemel it was unreal.
The 4 year old was used to going to nursery several days a week and had not long changed nurseries so was perhaps a bit more robust than usual. She has a history of being clingy so we were pleasantly surprised. Toward the end of the week we'd sometimes spy on her out on the mountain a few valleys from base cheerfully in a crocodile with her classmates - she had no problems coping at all and followed the instructions of her teacher just fine. A nightmare skiing with us though, ha - hence we only took her out the once of an afternoon. It was Enough. Yet DC1 would have been fine at that age out with us - again, it's just a personality thing. Two years later and I still wouldn't fancy taking DC2 out with us this year!
However I am a bit wobbly about whether our third child, who will be 4.75 when he skis in mountains for the first time next year, will find it. It could go either way. He doesn't settle into new childcare settings well at all, and that's without the complication of something as alien as a mountain environment and skis.
Most places definitely do lessons from four years old and a few do from three years old. I think that says all you need to know about how capable children are at particular ages. Although with the three year olds I think they spend some time playing in "snow gardens" and sledging with plenty o breaks for snacks etc and so on rather than the full length ski lessons which is daunting even for adults!
Just definitely research the ski school in question to find out how well the little ones are treated!