There's another video on YouTube (http://www.youtube.com/watch?v=JDQVN_G1bM4) of a guy flying a Cessna single in Utah in winter, with himself, 3 other adults and an infant. The carburetor iced over, they lost power and began descent. There was plenty of wide highway to use but the pilot opted instead for an adjacent snow-covered field (not an airfield), set down and immediately flipped. All aboard were shaken but unhurt, including the baby. The snow covered up all the field's imperfections and the gear dug into the irregular surface. I'd've chosen the highway, especially with the baby aboard.

It's a Cessna 150. I would say a D or E model.

Looked like the Cessna pilot was doomed after less than 1/3 of the attempted takeoff distance as the aircraft drifted left, possibly due to the ruts in the snow. Are you sure that this was a 172?