Do magnetic field slows in a medium?

As far as I know either you get a magnetic field to go through the material or you don't, suppose instead of say molten iron I am using drinking water maybe contains some traces of mineral such as iron etc as long as they are ferrous metal. I'm wondering what happens to the magnetic field of a permanent bar magnet when I drop it into the water, negate any oxidation? I know electromagnetic wave, light suffers from snell's law so how about the magnetic field which also travels at speed of light in vaccum condition?

It is very important to understand the difference between a static EM field, and EM waves (like light).

1. static field

You are asking about a magnetic field, EM field, which is a static field. The effects (if they would change) of the static field travel outwards from the source at speed c. This speed is not affected by the medium they are in, because this static field already exists everywhere around the source. The static field's effects are not mediated by real photons, but we use virtual photons to describe the mathematical model that we use for the static field. These virtual photons are off mass shell and are not constrained by the speed of light limit.

An electromagnetic field (also EMF or EM field) is a magnetic field produced by moving electrically charged objects.[1] It affects the behavior of non-comoving charged objects at any distance of the field.

https://en.wikipedia.org/wiki/Electromagnetic_field

1. EM waves, light

Now you are asking about EM waves, light, and you are correct, EM waves do slow down in media. Light and EM waves travel at the speed of light in vacuum, when measured locally, and they slow down in media.

The main idea really is that the changed phase velocity is a collective phenomenon that only manifests in macroscopic electric field, but is due to mutual microscopic interactions of the medium elements, while those interactions take place at unchanged vacuum light speed c.

Mathematics supporting the classical explanation of why the phase speed of light slows down in a medium

Now EM waves consist of real photons, that are massless, and travel at speed c in vacuum when measured locally. What really slows down in media is the wavefront of light. Individual photons do travel at speed c between the atoms of the media in vacuum (when measured locally).

In physics, electromagnetic radiation (EM radiation or EMR) refers to the waves (or their quanta, photons) of the electromagnetic field, propagating (radiating) through space, carrying electromagnetic radiant energy.[1]