Context. In the past few years, new methods that allow measurement of local magnetic fields in photospheres of distant stars have been developed. The first simulations of a small-scale dynamo in stars other than the Sun have also been produced. While the nature of the small-scale fields is still under debate, it is an accepted fact that they can be generated by the action of a small-scale dynamo in simulations. Aims. Our aim is to characterise the effects of the local magnetic fields in quiet regions of stellar atmospheres. Methods. We computed magneto-hydrodynamic and purely hydrodynamic simulations of stars of the spectral type G2V, K0V and M2V. The magnetic simulations were re-initialised from the hydrodynamical simulations, after adding the Biermann battery term in the induction equation to produce a magnetic seed that is enhanced by the action of the small-scale dynamo. Once the magnetic field was saturated, we compared the simulations with and without magnetic fields and characterised the differences in the velocity statistics, the appearance of granulation, and the mean stratification of a number of relevant parameters. These differences were also compared with the deviations produced by different treatments of the opacity in the simulations. Results. The saturation values of the magnetic fields are ~100 G for the three stars in their surface, which is consistent with the recent results for cool stars and other results for the Sun in the literature. The local magnetic fields have a negligible effect on the velocities of the plasma and the mean stratifications of the simulated stars. In contrast, they produce changes in the bolometric intensity of the intergranular lanes and the power spectrum at small scales of the temperature and vertical velocity of downflows. Significant differences between the hydrodynamic and magneto-hydrodynamic simulations were also found for the kinetic energy. This difference in energy can be explained by the transformation of kinetic energy into magnetic energy, which is consistent with the action of the small-scale dynamo.