I've been seeing more and more people using the word "Freestyle" instead of "Freeskiing".
Personally, I love it.
In the old days, it was "Newschool Freestyle" which denoted the passion for doing tricks and playful shit on the mountain. We used Newschool simply to set us apart from "Classic" freestyle, which meant moguls, ballet and aerieals.
Freeskiing in my mind was always a blanket idea, about not being held to one specific type of skiing. I used it a lot more towards big mountain and shit to differentiate from racing.
In the end, it should just be skiing. As J says - its just skiing.
However, if you feel the need to tell people that you like to play on the mountain, god damn do I like Freestyle better than Freeskiing. At least there's roots in that.