Justin: Wow!, you're talking some lightweight shoes. As an aside, how so you find them on summer trails (roots, rocks, etc)? I'll hike in anything for 20 miles, but over 25-30 miles in day and I found, long ago, that I (personally) needed a little stiffness in the sole or my feet felt beat up by the roots, rocks, etc. Hence I stepped up to Nike Lava Domes when they first came out and left the running shoes behind. Happily. But if those Vivobarefoot Neo Trails work on the trail, 9.2 oz would be fabulous! (per shoe or per pair?)
Dustin: If those Vivobarefoot Trails are as light as they look in the photo, I concur that it may be an uphill battle to make them work on snowfields. But I had an idea:
This isn't high-angle mountaineering, right? No front-pointing. Just something that provides some grip. Maybe a little floatation*?
*4 of us did a snow camping trip. All the same weight, similar pack weights. The two of us in size 11 shoes almost never plunged through. Both guys in 9 shoes plunged through frequently. Very easy going for us, very hard going for them because of slightly too little floatation for the conditions that day.
So here's the idea: 12" x 5" plywood under each foot. With wide straps to secure the light shoes onto the plywood. Maybe a heel and toe cup cut from a tin can. Some combo of lugs (made from plywood bits and gorilla-glued in place) and/or 3/16" bolts with their bottom ends sharpened into spikes. It would double the floatation of a size 9 shoe. <$10 of parts. So, after the snowy passes, you just throw them away, hand them to someone else, or burn them and pack out the bolts.
I'd see two design approaches:
Quick, dirty and cheap: 3/4" plywood, router out the space between the lugs, use velcro straps designed to secure garden hose and extension cord bundles.
Light and fully featured (maybe you mail them to and from yourself for the snow sections): 1/8" door skins on a foam core. Lugs and spikes on the perimeter of the bottom. Multitask the bolts by using threaded rod such that they project below to be spikes but project above to be heel and toe cups. And (I think this is a potentially cool idea): also make some foam-core wedges for side stepping on hills. 25 degrees or so would take so much of the ankle work out of traversing a hillside.