The desert snake basically has a continuous sine wave running throughout its body, apart from the tail and the head which are partially free - the head tends to stay fairly level but still inherits some of the rotation from the body wheras the tail flips loose. For the continuous sine wave, rather than using a wave modifier on a curve and relying on keying the speed (clumsy at best - I'd rather key the offset but then with speed set to 0 the wave disappears and further adjusting wave width during the animation isn't possible, unless you choose to scale the curve to change the wave width but then you get into more problems!) I drew a simple sine wave with a path, arrayed it many times, curve deformed it into a circle then applied the circular curve deform and set the path to be cyclic (on U). I then converted my circular wavy path to polygons and extruded it out (with shift-Z to constrain scale to X and Y only). I built a simple FK armature each of whose bones began and ended on the wavy surface, running round with a slight circular bend. Below the start and end of each bone I put an empty which was shrinkwrapped with Z project to the wavy surface. Each bone then has a track to constraint aimed at the empty nearest its tail.
I then use a second of chains of bones to convert this wavy (but curved) motion into a wave in a wave in a leaning plane (roughly the XZ plane rotated 45 degrees about Y) by copying only their local X rotation and making sure the bones in my second chain have their Z axes pointing towards the vector (0,1,1). Then a third chain of bones tracks to the tail of its double in the second chain with maintain Z up set. A fourth chain is used to add a user specified rotation in the world Z to each bone (for example a curve in the snake). This has to be done in a separate chain containing copies of the third chain's bones rotations as rotating any bone in the third chain disrupts all of its children's track to constraints!)
A final few bones are used to add non-automated animation to the head and tail. The width and height of the waves can be controlled by scaling (the parent of) the large rotating wavy disk in the world X or Z axis (there are some empties in between with maintain volume constraints to move the chain of empties which the first chain tracks to into the right position), and the rate of progress of the wave down the snake's body is controlled by rotating the wavy disk.
Now down to animating, at long last.