This guy has essentially solved that problem. He spent 3 years figuring it out. Basically improve on this and that is it.
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see update above, the first link died
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I’m pretty much convinced now that jet engines are the only real solution. And they can burn biodiesel you can make in your kitchen from leftover salads and lasagne.
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Anytime you find yourself using a huge jet engine on a project, it means you’ve missed the opportunity to use two huge jet engines on the project.
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Your terminology has disappointed me today 
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yeah I was thinking of making a DIY roller chain track using the methods researched here
Tracked PEV. Tank tracks, treads. Anything in the PEV spirit with a shitload of traction, so many many wheels may count.
That would have either rounded or square tread pieces attached depending on the use case. For a single track board that could self balance diy ow style a rounded track profile would be required. I have been pondering the effect that more than one contact point on the ground will have on low-speed turning needed for off-road riding. To fix this I figured two tracks would be side by side and you have a virtual pivot with springs or bushings to give lean to steer input at 0 speed (segway style)
long story short this thing I want to build could also make it ok on snow I think although more tailored to gnarly hill climbing.
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If you could get around the issue of burning your feet then mounting the jet thruster in the middle of the board with a turret and motor keeping it pointed with your direction of travel would be balanced for straight lines, full slides and park tricks.
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back to tracks.
nobody brought up the open source snowcat tracks yet?
They could be just strong enough for this application being nylon and kinda thick. US based replacements being nearly the best thing about it. Price overall also.
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Do you have a link?
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I think one track with the wedge shape on both edges starts to make it turnable. Then, I’m actually adding some (1 or 2) central bogey rollers mounted on gas struts towards the center to force the lower section of track down when you roll to either side. Hopefully this aids turning as you carve. Especially through loose powder. I hope that drive wheel works in pow and I can just go back to my day job and buy one. If not, maybe my prototype will have value in moving us towards realization of the e snowboard.
I know it’s not going to float forward on its own with this track beneath it. So I’m anticipating a powerful/high speed motor. It’s not going to be a snowboard, just like my eSk8 doesn’t ride like a skateboard.
About 4” thick without the track. The board might sit 5-6” above the surface of groomed snow.
What if you mounted a big jet engine on each side, so you could stand between them?
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I’ve seen enough Grizzy and the Lemmings to know that jets on a board (snowboard, hoverboard, whatever) go on the back, and there’s two of them. With two jets on the back using a slightly upward angle, I’ll bet the front would stop diving so much.
And the upward angle makes it easy for backflips, put on some exhaust flaps and you can even adjust your rotation speed
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to give you an unnecessary serious answer
Doubles the foot burning, one motor cutting out in a slide would throw you off, the opposite of the ideal central weight for tricks.
I was kinda thinking of cutting a hole in the middle and ducting the thrust backwards/down into the snow.
i think there is nothing prevents the electric snowboard now. there are a few models coming soon.
Do they use jet engines?
no need, just powered with motor which can offer a little bigger power is enough to push you riding fast on the snow