Can a permanent magnetic become too cold to function?

In the case of permanent magnets, there are two effects of temperature on the strength of the magnet:

• saturation magnetization
• coercivity

Both of these will be larger at low temperature, a stronger magnet.

A ferromagnetic material will order below its Curie temperature, often because of interaction between localized magnetic moments. The magnetization is saturated at $0$ kelvin. At higher temperatures, thermal excitations will flip some local moments so that the magnetization is lower. At the Curie temperature the long-range order disappears and the material is paramagnetic. This does not have anything to do with vibrations of atoms. It just depends on the strength of the interaction and the temperature.

A permanent magnet has a high coercivity. This is because the domain walls are pinned by metallurgical structures. The coercivity also decreases at higher temperature.