>>When the horse is racking, and he shows down and speeds up,
is he changing only the frequency of his steps, or does he also change
the shape of the stride? <<
Usually they change only the rapidity of the repetition of the steps,
although at slow speeds the support also changes from the fast rack (one
hoof, two hooves) to the slow or saddle rack( two hooves, three hooves). The
sequence and timing of the footfalls remains the same.
Having played around with this, it is possible for a horse to practically
rack in place (would be a piaffe if it could be in that gait) and then speed
up to 20 mph, with exactly the same timing of the footfalls. (have done it --
it was a major rush!) I have also seen paso finos (fino horses) ridden at
the same speed (very slow, just above stop) and change the cadence of their
footfalls from slow to fast back to slow -- it is enough to give you
goosebumps!