The interesting thing about snowboards are that they absolutely changed the culture and dynamics of skiing. The "freestyle" movement in the 70's had some impact but only a lasting impact in competition. Aerials and moguls are still events that competitors train for, but the ballet thing pretty much went away. I'm convinced that snowboards opened ski manufacturers eyes to the whole shaped ski revolution. Snowboarders opened the floodgates for half pipes and terrain parks. I give snowboarders credit for their effort in back-country (beyond the ropes), but skiers have always led the way in extreme skiing and always will. The truth is that the athletes all know that skiing is more versatile than riding a board. Now that boarders opened the doors to terrain parks, half-pipes and now the snowboard cross (4 racers on a demolition course in each heat) events, skiers are doing it all, too, and with more ability because independent legs just function far more effectively. Not that it doesn't look cool when a boarder rides like a surfer. There will always be that appeal.
Even the ski manufacturers have adapted. Skiers buy twin tips so that they are no longer restricted to skiing and jumping while facing downhill. Snowboarders DID blow the doors down. Skiers have followed, and embrace all of the avenues that are available (including traditional ski racing technique).
Will (edit actually, Tom!), I noticed that your daughter was also sitting or laying in the snow. While it seems to be necessary for boarders to constantly be planting their rear ends in the snow, I'm guessing that she was doing the same just to be polite!
Probably the largest objection that skiers have with regard to boarders is the habit of spreading across the trail with their rear ends in the snow and with backs to the flow of skiers every time they have to take one of their frequent breaks.
On a more serious, there is a culture divide between skiers and boarders that is probably more evident in urban areas. There are locations where the whole culture of boarding is actually pretty disgusting. Stand in a liftline that is dominated by boarders who are chain smoking and every other word is foul, and you'll know what I mean. I've seen them barging lines in packs and in many cases not bothering to purchase lift tickets. I've been to areas where the lift attendants actually seem to be intimidated because they will turn their backs and ignore infractions rather than enforce any kind of civility. It's not the teenagers ... it's the guys and some girls that are in their 20's and 30's that are the offenders. When you go to ski areas that are further removed from the urban areas, there is generally no difference between boarders and skiers (except the whole sitting in the snow to buckle your boots thing
). Perhaps that is why you get some surprised looks when people finally see a different side of it when they are removed from their local area.