The reason people are told to walk a horse that is colicing, is to allow the horse to move, thus perhaps helping the blockage work its way out. I find lunging a horse for a short bit at a trot often helps get things moving.
It has been in the last few years that vets are now realizing that twisted gut does not happen from the horse rolling during a colic episode, but twisted gut often happens prior and the colic is only a "symptom" of the twisted gut.
If a horse is laying down quietly, that is fine, as long as they aren't thrashing or rolling violently.
Also, walking a horse continually who is already stressed from a colic episode is not necessarily good either. I have actually seen some owners walk their horses into exhaustion. They are all ready stressed, most times hot, sweaty and simply walking them over and over and over and over, can prolong the colic episode.
In any colic case you need to call your vet ASAP. Take your horses temp, respiration rate, check their cupillary refill time, color and moistmness of gums... thisare all things vets need to know right away....as it will help them assess the severity of the colic episode.
Horses are like chips...you can never just have one