Lots of good advice here. I just taught my grand daughter this weekend, she's 4 and more athletic then any child I've ever known.
I have two boys that are now 22 and 25 and I taught them. I put my first boy in lesson's at 2.5 years old (they took them from 2 to 5) and i was so mad at the instructor when he didn't ski at the end of 8 weeks. My bad; kids that age don't learn and i expected a lot. I didnt' teach then. 2 years later I was an instructor and my second boy played in the kinder ski park until he was 4.5, when I then taught him in an hour. He had been dying to go up the big hill with the rest of us for prior two years and was atheletic and learned. The he passed the first child's ability quickly. So...don't push it, make sure they have fun. My first son we swtiched to snow boarding when it was obvious skiing would never be his thing.
Children tend to learn in one hour at the age of 5. Prior to 5 the rare one learns that quickly, most don't. I know this now, because I'm an instructor who taught lots of kids!
I had one group of 3 year olds for 8 weeks once and promised all parents they likely wouldn't ski by the end of it but would have a great time playing in the snow, standing and walking around, sliding on gradual slopes. i had all 8 children going down all hills at the end of 8 weeks. That is the only 3 year olds I ever got going so well and I taught for over 10 years. It was at a private club, i had two assistants who did lots of picking up kids and playing and helping on lifts. The parents of these children went home every week asking what they could do at home during the week and all put their kids out in the yard on skis daily to play. I'm sure this helped.
Aside from this, any child I did teach prior to the age of 5, including my own, seemed to need re taught at the beginning of each year. AT 5 they seem to retain the prior year and advance. So those 3 year olds came back at 4 and had to get a lesson on turning and stopping and spend a few days learning again. The 5 year old seems to come back at 6 and need a run or two on the baby hill to get comfy and away he goes, advancing for the year and not relearning anything.