My 1st rough,off the top of my head attempt at a winter SUL list came out to almost 8 lbs. This will be a challenge, indeed.
I'm not counting weight of transportation-- I assume skis or snowshoes, which would be worn except for (hopefully) short stretches. This does imply a pack robust enough to strap them on. A snow shovel would be included--I have a 5.75 oz. one in mind.
Above timberline---an Ice Axe I usually would have because I would want to do some ascents ( but I'm in the Pacific NW). No climbing or icy cols?
Weight ,weight, weight.
Alcohol Stove--is there one capable of melting sufficient snow in these conditions? I have no personal experience,here. I would be carrying a canister stove but that, too, will push the weight too high. I hate fussing with fires for cooking in Winter. And above timberline, use of wood is not really kosher.