I have to disagree with the writeups above. In my own experiences in the upper Midwest, the flexible flyer is only good for running on ice, or on snow that has been packed down by other sledders. If you try to run a flexible flyer down a hill with fresh snow, then you are most likely going to have one or both of two problems:
  1. If the snow is not deep enough, the runners will sink straight through the snow, and run on the grass and dirt beneath.
  2. If the snow is too deep, the wooden bar will drag in the snow above, spraying your face with more snowdust than is fun. In the worst case, the sled will become completely submerged in snow, and will barely move at all.
In my experience, the flexible flyer is outclassed by the inner tube for smoothness of ride and hang time off jumps, the carpet sled for control and excitement (see the last part of The_Custodian's writeup above), and the saucer sled for sheer terror. All of these sleds perform admirably on deep and/or fresh snow, due to the fact that they disperse the weight of the user.

The only exception to this is when you decide to sled over very hard-packed snow or ice, which is when the thin runners of the sled show their true worth on control and speed. This is also a good place to mention the enormous increase in injury potential that you get when you choose a flexible flyer: (hard wipeout at high velocity) + (cheap wood and metal vehicle) = emergency room visit