I'm not an engineer or designer, but have been on snow enough to know that even packed snow--even east coast boilerplate, I imagine--isn't fluid, and what a ski kicks up from it is not 'dust.' Even in cold smoke form, snow isn't anything like the Platonic ideal of a flat surface you assume is present somewhere in the world. For instance, the smoothest, most consistent surface imaginable is made up of bits that are more compacted by grooming machines than others, and previously skied tracks contain melted and refrozen water crystals. Even if your stunning skis plane beautifully through water or air, the margins of the cutouts are going to catch on the surface's lumpiness, acting as additional ski edges which direct the ski according to their orientation to the direction of the ski. Forgetting for a moment the stress this would place on the ski's materials, it's hard to imagine that it would contribute to a smooth ride of any kind.
Then you have to consider that it's impossible to ski without varying the angle between snow and ski. Skiers don't ski with perfectly flat skis, and even clean carving displaces snow beneath their ski's outer edge. Softer snow yields a deeper track, to run against a wider area of the ski, and you have to consider the combined interactions of each area of each cutout's edges when just a portion of the ski is in contact with the snow to know how the ski will run in each situation, and each effect would have to cancel every permutation of the others if the ski is to be controllable.
It's not an impossible exercise, but I do wonder whether you've had this kind of analysis done. There are similarities between designing a surface to interact with water or air, and some of those designs apply to solid materials like snow, but the solid and varying nature of snow is such that cutouts which would cut beautifully through water will make the skiing experience pretty miserable.
Of course, the solution would be to come up with a transparent analogue to p-tex for the bases so that the cutouts would be solid p-tex, and the rest clear p-tex layered under your other materials. It would still make for an attractive ski, but nothing like the spare beauty of your design. On the other hand, if I could afford such a sculpture, I'd snap the current version up in a heartbeat just to display in my home.
By the way, I'm not concerned about your lack of fluency in English or errors in your website. I find myself digging up fascinating works in progress all over the web, and it's the nature of the Internet that preliminary work by non-English speakers includes descriptions in broken English. This is a work in progress, and not designed as a pitch for anybody, just stimulation for feedback. I think it takes a lot of confidence to put draft work out there for everyone, including potential final users, to see and take a bite at, and even more to try to describe it in a foreign language. I'm sure you get a lot of good feedback, and I'm sure you get a lot of flack, too.
Best of luck in your work!