Magnetism, part of electro-magnetic spectrum, of which visible light is a small part, and its field of force moves at the speed of light, 300,000 km/sec, or 186,000 mi/sec.
But, does magnetization in a wire/metal propagate at the speed of light?
The answer is no; it propagates along at the speed at which each of the individual atoms can align their own polarity.
If you ask, "Do changes in the magnetic field propagate at the speed of light?"
The answer is a resounding yes. If an enormous and powerful magnet suddenly appeared one light year away, then it would take exactly one year for magnets on Earth to feel its pull. It would take one year for the "magnetic force" to reach the Earth.