To me, the most negative course of action to take would be to attempt to segregate the mountain. This will only cause bitterness and heighten any tension that might exist between riders and skiers, or older and younger people on the mountain. Maybe the people that complain the most should think back to the time when they were young. It might be possible that they rode with the same sense of abandon that they are complaining about now. By and large, I think all the people that use the mountain do share it in harmony.
Cats seem to do a lot better alone at home than dogs do.
That said, I didn't know cats weren't OK at Burton. Maybe the dogs put in that rule. I love mountain biking, but honestly I'm probably more passionate about surfing. Ski manufacturing should be left to the ski companies.