If a horse is pacing fast the rider will be rocking side to side. Actually once a horse approaches racing speeds at a pace it will smooth out. Until it approaches racing speeds it kind OMG! And wrap your hands into the mane and wish you had some place to wrap your toes too.
Look at some of the speed racking videos and standardbreds racing under saddle on youtube.
Moni Maker is a trotter but she is great to watch anyhow. Notice her trot looks quit different from a horse trotting down the trail.