Stanton Peak lies on a virtual "island" between Virginia and Spiller Canyons, just west of Virginia Pass and the Hoover Wilderness. Geologically, the setting is similar to the Mount Dana/Mono Pass/Parker Pass region to the south -- along the ancient boundary between the intruding granite Sierra Nevada Batholith and the existing sediments, now metamorphosed (metasediments). In fact, Virginia Peak, Stanton's nearest northern neighbor, is vertically bisected by the granite/metasediment boundary. Although the "metaseds" bring a splash of red to the otherwise drab gray granite surroundings, they are generally inferior to granite for climbing: loose and brittle.
Stanton Peak is a straightforward and non-unique class 2 scramble from all points to the north, south, and east. The sheer west face, made U-shaped by the Pleistocene-era glaciers which sculpted Virginia Canyon, likely boasts one or more multi-pitch technical climbs, though yours will likely be the first ascent!
The easiest access to this region, and the one we used, was the Green Lake trailhead in Hoover Wilderness. To get there, go south from Bridgeport, where you pick up your wilderness permit, about seven miles and turn right onto USFS road 142. The sign, which is small and easy to miss, reads "Green Lakes". Follow the bumpy-but-passable-by-passenger-cars dirt road to the Green Lakes trailhead and campground. Parking seemed adequate given the demand.
Given the extreme remoteness of this region, public transportation options are limited, if nonexistent. YARTS, the Yosemite shuttle bus, runs from Merced, with Greyhound bus service, all the way over the Sierras to the city of Lee Vining. Unfortunately, at this point you are thirty miles--much of it on desolate dirt roads--from the trailhead.
For more information on the approach from Green Lakes Trailhead to the base of Stanton Peak, check out the "approach" section of the South Ridge route.
The real issue in winter is access. I don't know when Green Lakes Road opens, but you have to imagine that the snow melts a bit earlier on the eastern side of the Sierra. Also, the trailhead is only at 8200', so it might have good accessibility by April or so--well in time for some great corn skiing.