An external magnetic field will effect the permeability of any core used, if it is saturated its relative permeability become one. If you use a short circuit coil and magnetically link it to the field of the coil, the apparent inductance of the coil will fall. Like wise if you introduce a piece of ferrite, the value of the inductor will seem to rise.
An external field out side of the above cases will have no effect UNLESS specially engineered. i.e. a coil carrying a certain frequency is purposefully linked to another source of that frequency which will then modify the current in it so the inductors value seems to have changed.
Frank