I think rather their metaphysical state, their non-corporeal form, as it were, has some supernatural aspects similar to wolves. That's not a suit, that's just another layer of the form in which one exists in life. On some humans, it has the qualities that relate to the One Power, in others, it lets them sniff or see Min's viewings and in still others, it is constructed very like that part of wolves that runs around in Tel'Aran'Rhiod.
Well, that's because wolves don't have souls in the human sense. They exist on a metaphysical level as all living things do, but the part that makes choices and thinks, isn't the same.

Or merely spirits. There's the body, which is the part that has matter, the spirit, or part that dreams and uses the One Power and connects through the warder bond and is afflicted by Compulsion and the soul is the thing that keeps on going and ultimately makes the choices. It is the thing that is contradicted with Compulsion, the thing that WANTS to lie or channel to kill and the Oath Rod won't let it. Without the soul the spirit or body can't live. I think the Ogier Verin touched in tGS managed to leave his spirit in his body but his soul moved on. I think it is the spirit that goes into T'A'R and the Heroes retain it between their lives, which is how they remember when they are in T'A'R or responding to the Horn and why they are not constrained by the same physical limitations when they come to the Horn. I also would guess that's why channelers don't necessarily carry their strength in the Power from life to life, but Rand does (he takes his Spirit to T'A'R with the other Heroes) and the Forsaken retain their spirits when they are transmigrated.

Jordan or his characters just use sloppy terminology. I don't know if wolves have souls, but they do have spirits.