Icelandic Horses, with the wide range of gaitedness (or non-gaitedness) in the breed, have the potential of being able to "fox walk".
The more diagonally gaited horses may show fox trot, fox walk, or fox rack, as their natural gaits.
Lee Ziegler, gait expert, tell us about the fox walk:
The "fox walk": This is really just a slower version of the fox trot, done with a slightly longer time interval between the set down of the front hoof and its diagonal hind. It looks and sounds like the fox trot, with the same uneven 1--2-3--4 timing.
The "fox walk": Again, this is very similar to the fox trot, just done at a slower speed. The horse will almost always "cap" his front track with his hind in this gait. Top speed is probably no more that 6 mph in the fox walk.
"Fox walk": This is a smoother version of the fox trot, with less "push-pull" motion and a less well defined "stutter step." Again, there is no side to side motion in this gait, and less "bounce" to the hind quarters than in the true fox trot.