I got an reply from the winter sport manager for the Mt. Adams Ranger District after asking the same thing and he said this: "Cold Springs Campground, where the South Climb starts is currently under 3meters of snow. No wheeled vehicular access is possible within 13 miles ofthe South Climb. Cold Springs Campground is accessible via snowmobile.The road access, when covered with snow is a steep, narrow side hill andshould only be attempted only by highly skilled snowmobile operators. TheSouth Climb is usually accessible via wheeled vehicle in late June."
So there you have it.