Thais never eat snow.
For obvious reasons.
I would have put the kid into a figure four arm bar and announced “You’re Done”.
Ignore it. You’d be right to let the parent know if the kid was eating dog poop or picked up a hypodermic needle, but eating fresh snow…even if you wouldn’t want your kid doing it, it’s such a minor thing that it would be rude to say something.
Think of something that your kid does and imagine how you’d feel if another random person told you that you shouldn’t let your kid do it.
I’m going to take a WAG that you don’t have kids because people do it ALL THE TIME. When you have kids you get random parenting advice for no effin reason. I mean, I was in line at the store one day and the lady behind me told me I shouldn’t feed my kid baby food. I should grind up fresh fruits and veggies instead. Ya know what lady…MYOB.
Can I have your autograph!?
For some reason, I parsed this as the Massenet title character talking like Tarzan.
This made me laugh out loud.
.
I ate snow when I was a kid. A mouthful of snow on the playground isn’t going to cause hypothermia. I’m in the MYOB camp. BFD.
Speaking as the parent of a little kid, if you were really concerned, you could have said something fairly neutral, but in a way that I would have my attention called to the behavior, something like “wow, she couldn’t wait to start eating that snow, eh?”
And then I would say “yep, she’s pretty into it” and then you could rest assured that I knew, and wasn’t concerned about it.
Why in the world would you feel the need to say anything at all? What is the danger here?
Damn it man, can’t you read? It’s* snow*!!!
You know nothing, Jon Snow.
For extra laughs, you could shout “Finish!”.
We did this when we were kids, we called it snow custard.
If we could somehow automate this as the default response to every “what should I do?” thread on this board, it would save a lot of time.
babality!
Nice.
And after that you could all leave the kids outside on the sidewalk in their strollers while you get to know her over a drink in the pub.
Nuke the entire site from orbit. It’s the only way to be sure.
Finnish? 
Cultures differ so dramatically that it’s difficult to generalize. Given that the US Dopers don’t even get the “don’t eat the snow vibe” in Finland, our opinions about Finnish childrearing is probably useless.
Some cultures are very “it takes a village” and if your rugrat needs a scolding, any nearby adult will do. US culture has lately acquired this weird phobia about adults interacting with other people’s children (especially males) and there’s some general touchiness about critiquing other people’s childrearing skills as well. (If you have a convenient nephew handy, you probably have a bit more latitude than if you’re a single adult.)
So, if you were in the US, you pretty much did all that you were expected to do and a bit more, given that the kid wasn’t in any actual danger.