reseating beads:
Hard way:
Use your bottle jack and a 2'x2' base (plywood is fine).
Jack up axle that has the blown bead. On snow, sometimes even the base will sink in the snow, you might need to get creative.
Get the tire free and try to get all snow, muck from off the rim and bead.
Wrap ratchet strap around the circumference of the tire in the center of the tread and start to compress the tire. You are trying to squeeze the bead against the wheel so it will create a seal when you are filling with air.
Start filling the tire. The best way to do this is to have CO2 bottle with the regulator cranked way up for blasting a large volume very quickly. On-board air with a tank is the next best thing. QuickAir or like 12V compressor is very challenging.
The key is to get a clean rim/bead connection.
Last snow run I was on I lost a bead twice on Marni's 5.9 doing massive stupid AWD donuts. I reseated the bead only with using the CO2 (no jacking, no ratchet strap).
Fast way:
Involves removing wheel from vehicle and a flamable gas. I have only seen this done, never tried it. I wouldn't recommend it, but in a pinch it works. I have heard that the valve core should be pulled while doing this so the vacuum caused after the initial explosion doesn;t suck the bead back off.
Either way, a bottle of CO2, a good quality ratchet strap and a stable jack base are essential for snow wheeling. You have to be prepared if you are in the back country in the Sierra in the wintertime. It's no place for amatures.
Also, avoid any cotton clothing altogther in the snow. Once cotton is wet, it will not dry out and will wick BTU's from your body very quickly. Once you are cold, your are in serious trouble. Best is a breathable waterproof fabric like Goretex (or knockoff). Wool is a good second. Cotton=Death.
Be careful, have fun, and be prepared for any eventualilty
SeanP