For a normal coiled electric cord, the induced magnetic field is next to nothing due to the neutral return also being coiled with the cable. The net current through all the conductors in the cable is zero (absent a ground fault), so no electromagnetic induction takes place.
A coiled welding cord is different since the other current carrying conductor is separate. It would induce a magnetic field and could thereby cause inductive heating and other difficulties.
The possible danger from coiling a cord comes purely from resistive heating and the increased difficulty of that heat dissipating from the coil. With an appropriately specified cable (which needs to take into account the close quarters its sitting in), that should not be a problem unless there's some physical damage to the cable.
