Great move Dad! I started skiing with a helmet when my son was little and it was time to teach him. I didn't want to be a hypocrite so I bought a helmet. That was 15 years ago. Since then I've owned perhaps 7 helmets. I'm currently wearing a Smith Vantage and I like it a lot. Here are some of my priorities for helmet purchase (more or less in order):
Fit (I have an oval melon - some helmets are generally more round (Boeri, POC), some more oval (Smith, Giro). Also, do the straps work well around my ears and clasp well under the chin.
Vents - I sweat when I'm skiing. Even when I lived on the east coast I hated helmets without vents because they just insulated too well. I like having the ability to close the vents on a deep, cold day. Similarly, I like removable earpads. I leave them home and keep a thin headband in my coat on cold days in case my ears get cold.
Weight - heavy = bad. No, you should not use your motorcycle/snowmobile helmet skiing.
Goggle compatibility - Do the goggle fit in the helmet. And does the helmet have a goggle strap retention device (something on the back holding the strap on, in case they flip up and try to fall off the back of my head).
Looks - gotta look cool. Speaking of cool - I've also found that white helmets seem slightly cooler in the spring sunshine than black/gray helmets. It probably doesn't make much difference, but at least psychologically it makes sense to me.