In the framework of magneto-photonics, the optical properties of a material can controlled by an external magnetic field, providing active functionalities for applications, such as sensing and nonreciprocal optical isolation. For noble metals in particular, the inherently weak magnetooptical coupling of the bulk material can be greatly enhanced via excitation of localized surface plasmons (LSP) in nanostructured samples. Hyperbolic metamaterials therein provide the ideal platform to tune the plasmonic properties via careful design of the effective permittivity tensor. Here, we report on the magnetic circular dichroism of electric and magnetic dipole modes of a type II hyperbolic metasurface. Disk-shaped nanoparticles consist in stacks of alternating dielectric and metallic layers. Using an effective medium theory, we show that the optical properties of the system can be perfectly described by an anisotropic homogenized permittivity. Magnetic circular dichroism spectroscopy experiments are compared with plain gold disk samples and reveal a broadband magneto-optical response across the visible and near infrared spectral range. In particular, derivative-like spectral signatures at the resonances of the nanoparticles prove the induced dichroism for the two modes of the system. Results are interpreted in terms of magnetically induced spatial confinement/broadening of circular currents in the nanoparticles and are compared with a comprehensive numerical model based on the finite elements method using the real dimensions of the nanostructure. Spherical particles are employed as an analytical model system, allowing to generalize the contribution of electric and magnetic modes to the total magneto-optical response. More in detail, interaction cross sections are calculated as a weighted sum of the corresponding Mie coefficients. Utilizing a perturbative approach, we describe the magneto-optical effect in terms of linear changes in the cyclotron frequency of free charge carriers in the metal. By comparing our analytical model with full-wave numerical results, we can identify the contribution of electric and magnetic dipole modes to the spectrum and reproduce the spectral line shape we observe in the experiments for the hyperbolic nanoparticles.