I was looking at a snowboard film this weekend and they had a part where they were using boards similar to snowboards but without being strapped in. I looked into it and is a whole other sport entirely. The ones on the video I saw were really long and more like a longboard/cruiser than a normal skatie. Here is a video on people just mucking around on snow skateboards, which are the little ones and are more or less a normal skateboard with no wheels and you can pop your board really well. I am more interested in the longer boards that the smaller ones. As they are wider which provides more foot space and it would be easier to carve I imagine. The normal small ones are around $200 and look pretty fun. I am looking out for a long one though and I want to attach a leg rope to it. I might buy one for my next snow trip and let you guys know how it goes.
Here is a video for you guys to get a general idea. I will be uploading more snow skating videos (Hopefully the longer ones which are crazy and can get really good air)