Context. Efforts to compare polarization measurements with synthetic observations from magnetohydrodynamics (MHD) models have previously concentrated on the scale of molecular clouds. Aims. We extend the model comparisons to kiloparsec scales, taking into account hot shocked gas generated by supernovae and a non-uniform dynamo-generated magnetic field at both large and small scales down to 4 pc spatial resolution. Methods. We used radiative transfer calculations to model dust emission and polarization on top of MHD simulations. We computed synthetic maps of column density N_H, polarization fraction p, and polarization angle dispersion S, and studied their dependencies on important properties of MHD simulations. These include the large-scale magnetic field and its orientation, the small-scale magnetic field, and supernova-driven shocks. Results. Similar filament-like structures of S as seen in the Planck all-sky maps are visible in our synthetic results, although the smallest scale structures are absent from our maps. Supernova-driven shock fronts and S do not show significant correlation. Instead, S can clearly be attributed to the distribution of the small-scale magnetic field. We also find that the large-scale magnetic field influences the polarization properties, such that, for a given strength of magnetic fluctuation, a strong plane of the sky mean field weakens the observed S, while strengthening p. The anticorrelation of p and S, and decreasing p as a function of N_H are consistent across all synthetic observations. The magnetic fluctuations follow an exponential distribution, rather than Gaussian characteristic of flows with intermittent repetitive shocks. Conclusions. The observed polarization properties and column densities are sensitive to the line-of-sight distance over which the emission is integrated. Studying synthetic maps as the function of maximum integration length will further help with the interpretation of observations. The effects of the large-scale magnetic field orientation on the polarization properties are difficult to be quantified from observations solely, but MHD models might turn out to be useful for separating the effect of the large-scale mean field.