In your example, the relevant speed isn't the speed of propagation of disturbances in the magnetic field, but rather the speed of the alignment of iron atoms.
You are really asking "Does magnetization of a wire/metal propagate at the speed of light?"
The answer is no; it propagates at the speed at which each individual iron atom can align its polarity.
If you are asking, "Do changes in the magnetic field propagate at the speed of light?"
The answer is yes; if a giant, huge, powerful magnet appeared one light year away out of nowhere, then it would take exactly one year for magnets on Earth to feel its pull (however small it may be). That is, it would take one year for the "magnetic force" to reach the Earth.