I disagree that mogul skiers should not be counted as freeskiers. True, the sport has rigid scoring guidelines and a carefully formatted course, but it also allows for the development of an infinite range of styles and trick combinations. Similar to competitive slopestyle and pipe skiers, mogul skiers spend countless hours training for, visualizing and perfecting their runs. Saying that they for a skier to be a freeskier, they can't belong to a specific discipline discounts any skier who has an interest in competing.
As to the larger question of what makes a freeskier, I would say that there's no strict definition. The concept of freeskier used to include the discipline of ski ballet, for instance. You don't see anybody doing that anymore, but does that mean that the guys in Hot Dog the Movie were not freeskiers? No way. For me, being a freeskier means going out as often as I can (to a mountain, or a friend's backyard) and trying to improve. I could be sessioning a rail in the park, lapping the pipe, charging a line of moguls, or even skiing switch down a groomer. All involve elements of freestyle, so I guess that's what I would consider to be the unifying concept.