Regarding the Tennsessee Walking Horse it is a huge no-no to let them trot:)
Here's the preferred gait - the running walk
Stepping Pace - a huge no-no with many Walking Horse folks but not me. This is a Morgan, my 21 yo TWH has a stepping pace every bit as smooth as the running walk my other two Walkers do.
Just an FYI, when a Walking Horse is truly performing the running walk as its intermediate gait, it's head will bob up and down in varying degrees that depend on the horse.
If it is performing the stepping pace or the rack, the head bob is from side-to-side and can also vary from very subtle to no-so-subtle.
I am of no help in describing the foot falls even when I watch them. I have to hear them to know.
I can say that a hard lateral pacer will move its left side then its right side, consistently as someone has already mentioned:)