Man, that's my worst nightmare, stuck on some snow covered fire trail where it's real tough to get out.
I don't own a Snow-Trac yet, but I have 35yrs of VW experience. I hate to sound like some know-it-all, blow-hard, but if I don't mention my experience, my advice might be dismissed. I've worked on air-cooled VW's as a hobby for years, have done the infamous VW Bus
Shasta Snow Trip 3 times, and numerous long distance endurance rallies with air-cooled VW's, two of them were 1500mile 24hr under-the-radar, boot-leg races from Vancouver BC to Ensenada Mexico. I also drag race VWs and race at Bonneville (check the March 2013 cover of hotVW's magazine, upper left cover, and contents page is the yellow Ghia I drove to 156mph last September) We always carry spares.
For troubleshooting an older carbureted and points ignition engine, don't under estimate the efficiency and power of having known good spares.
Carb: Starting fluid... if it will run while spraying starting fluid into the air horn one spritz every 2 seconds while working the throttle, but dies when you stop spritzing, you have a fuel delivery problem. I'm not sure about icing, but I did have an old Baja bug (exposed engine) that I'd take skiing when I was a teen, who's carb would ice and it would refuse to idle. It would pop, sputter, and not run well, loosing the ability to idle, then the mid-range circuit would work. It would sort of run if I pumped the throttle and kept the rpms high, running off just the accelerator pump and main circuit. Pouring hot coffee directly on the exterior base would de-ice it, temporarily at least, until I could get to lower and warmer elevation.
Spark: If you remove the coil wire from the distributor, hold it 3/4" away from a decent ground, you should get a snappy blue spark bridging the gap 2 times per engine revolution. If not, may be an ignition problem. If you need to move the conductor to 1/4" or closer, and/or the spark is yellow and lazy, you have weak ignition from closed up points, low battery, bad ground, etc. No spark at all can be many things, including those above. But it sounds like you have spark some times.
The most common culprit is closed up points, that just need to be re-gapped, and you're on your way. But if you have a weak fuel pump, spark plugs that are now fuel-fowled, a weak battery now, you can have a couple problems to sort at the same time.
Points: The cheap inferior rubbing block material used in modern replacement points is the culprit that leads to points closing up. A dab of dielectric grease (using a Q-tip) on the points cam/rubbing block usually help stave that off for longer periods of time. Only use genuine Bosch ignition parts on air-cooled VW's, follow this and you'll be happier. The Pep Boys and Napa replacement parts use aluminum and steel cap n rotor conductors, that don't work well with the old VW ignitions, from my experience. Bosch uses copper and brass. The same with points, if you use points. I like Pertronix units.
Pertronix units: Pertronix ignitions modules retrofitted into a stock VW distributor have been good to me over the years, but a friend of mine, who works on acvw's for a living today, has not had the same good fortune. He sees pertronix ignition module failures on customer cars all of the time, he says.
Spares: On every VW endurance en devour I've been on, we always carry what we lovingly refer to as our 'crash box', or a 'possibles box'. Included is a known good used distributor, fully set up with spark plug wires, numbered, that has been previously run and timmed on THAT engine. When I say set up and timed, I mean with the locking ring clamped in place that stays with the spare distributor. That way, the replacement distributor is truly plug-n-play with nothing more needed than a 13mm socket and extension, no fiddling with the clamp with cold fingers, no setting of timing or adjusting points, or swapping over possible bad ignition parts from old to replacement distributor. Same with a spare carb, run-in and adjusted for THAT engine, drained of it's gas and brought along is cheap insurance.
I hope you get it fixed on the trail, and can self-recover it. Good Luck!
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