We have a local ski hill that does lessons for young kids. I say "hill" on purpose - it's not part of a mountain ski area (although we have those a little father away). But it doesn't have the chaos of a large area for a whole variety of ski levels. They have some tubing and some short runs, so it's great for amateurs and kids of all ages.
I think the key with little kids is that they not get so horribly cold, they not have a 2 hours drive to get there every time, and they not feel that, once there, they are at the ski site for the entire day. It's too much for them. So places that you can go for 2 hours, practice, and be successful early on are really awesome for getting a fun taste of it. If they love it, great. If they truly hate it, then you haven't invested a lot of money in skis, lift tickets, gas and overnight accommodations.
I agree with Doris Day that learning without poles is best - otherwise there are too many things for them to coordinate. If your kids go to preschool or some other program where they are accomplished at listening to someone else, separating from Mom and Dad, and focus on what's in front of them, you can probably start. If they are always off running in the opposite direction, and if they fight you about getting bundled up in winter gear, they may find skiing frustrating at this age.
And I agree to check with the closest ski places to see what the averages are. However, some places really push kids too young because they make the money whether or not your kid gets frustrated and goes home.
If you want your kids to be on skis early so that they get the early love of it and more years to develop skills to enjoy it, that's great. There are some parents out there who are determined that their little ones will be Olympians, and no one wants to be in a class or on the slopes with them! So be sure that whatever place you choose is looking to foster enjoyment and enough decent skills mastery that they don't get hurt, rather than a place focusing on training ski team members for competition.