I know when you pass a current through a length of copper coil or a solenoid, there is the induction of a magnetic flux. But what of the coil made of the ferromagnetic material, the permanent type magnetic material? Is there superposition? Is there Interference thus resulting in the cancellation of the overall field?
I suppose your question corresponds to a DC current. In that case, if you have a solenoid made with ferromagnetic wire, you have at the core of the solenoid the same field than in a copper solenoid. But while the magnetic field INSIDE de copper is very small, when using ferromagnetic wire the B field inside it is great. In DC circumstances there are no more differences. By contrary when working with AC current the problem is more complicated. The current density distribution in the ferromagnetic wire experiences the well-known skin effect, which frequency dependent. This effect is more noteworthy in iron than in copper due to its higher magnetic permeability. Therefore, the magnetic field inside the ferromagnetic wire behaves in a more complicated way, while the spatial dependence of the field in the core of the solenoid is like in DC.
Do you mean a coil in which conductors are made of ferromagnetic material instead? If that's the case, you would probably not be better off: the field which is created is concentrated around the conductor (mostly at core of the solenoid) and in another direction, so it would not benefit from the increased magnetic permeability (which is what ferromagnetic materials in solenoids are about) as it wouldn't be "on its path"; it would still be "hard" to create a magnetic field in that direction.
This is my general understanding, I would wait for an answer with more evidence.
P.S: Using ferromagnetic materials would increase the coil resistance and hence reduce the field for the same voltage.